October | October | October | October | October | 1 - Mathematical Physics Seminar
- Seminars
12:00 am-1:00 pm 11/01/2019 - CMSA EVENT: Quantum Matter Workshop
All day 11/01/2019 Please note: this workshop has been postponed to a later date. Details will be posted to this page when they are available.Throughout the summer, scheduled speakers for the Quantum Matter Workshop will give talks on Zoom for the Quantum Matter/Condensed Matter seminar. The CMSA will be hosting our second workshop on Quantum Matter. Both of these workshops are part of our program on Quantum Matter in Mathematics and Physics. The first workshop took place in December 2019, and was extremely successful, attracting participants worldwide. Learn more about the first workshop here. Organizers: Du Pei, Ryan Thorngren, Juven Wang, Yifan Wang, and Shing-Tung Yau. Speakers:- Mathematical Physics Seminar
- Colloquium
5:00 am 11/01/2019 No additional detail for this event. - CMSA EVENT: Workshop on Quantum Information
8:00 am-6:07 pm 11/01/2019-04/24/2017 The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 21-22. You can find more information here. Register for the event here. The following speakers are confirmed: - CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
8:30 am-5:20 pm 11/01/2019-08/20/2018 On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B. Saturday, August 18th: A day of talks on Vision, AI and brain sciences
Monday, August 20th: a day of talks on Math
Speakers:- Stuart Geman, Brown
- Janos Kollar, Princeton
- Tai Sing Lee, CMU
- Emanuele Macri, Northeastern
- Jitendra Malik, Berkeley / FAIR
- Peter Michor, University of Vienna
- Michael Miller, Johns Hopkins
- Aaron Pixton, MIT
- Jayant Shah, Northeastern
- Josh Tenenbaum, MIT
- Burt Totaro, UCLA
- Avi Wigderson, IAS
- Ying Nian Wu, UCLA
- Laurent Younes, Johns Hopkins
- Song-Chun Zhu, UCLA
Organizers: Publication: Special Issue: In Honor of David MumfordGuest Editors: Ching-Li Chai, Amnon Neeman - CMSA EVENT: Big Data Conference 2018
8:30 am-2:50 pm 11/01/2019-08/24/2018 1 Oxford Street, Cambridge MA 02138 On August 23-24, 2018 the CMSA will be hosting our fourth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The talks will take place in Science Center Hall B, 1 Oxford Street. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants. Please register here. Confirmed Speakers: - Mohammad Akbarpour, Stanford
- Emily Breza, Harvard
- Francesca Dominici, Harvard
- Chiara Farronato, Harvard
- Kobi Gal, Ben Gurion
- Jonah Kallenbach, Reverie Labs
- Samuel Kou, Harvard
- Laura Kreidberg, Harvard
- Danielle Li, MIT
- Libby Mishkin, Uber
- Josh Speagle, Harvard
- William Stein, University of Washington
- Alex Teyltelboym, University of Oxford
- Sergiy Verstyuk, CMSA/Harvard
Organizers: - Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
- Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
- Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
- Jun Liu, Professor of Statistics, Harvard University
- Horng-Tzer Yau, Professor of Mathematics, Harvard University
- CMSA EVENT: F-Theory Conference
8:30 am-3:00 pm 11/01/2019-09/30/2018 The CMSA will be hosting an F-Theory workshop September 29-30, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Click here for videos of the talks. Organizers: Speakers: - Mirjam Cvetic, University of Pennsylvania
- Tommaso de Fernex, University of Utah
- James Gray, Virginia Tech
- Jonathan Heckman, University of Pennsylvania
- Monica Kang, Harvard University
- Sándor Kovács, University of Washington
- Anatoly Libgober, UIC
- Matilde Marcolli, Caltech, University of Toronto, and Perimeter Institute
- Washington Taylor, MIT
- Cumrun Vafa, Harvard University
- CMSA EVENT: Workshop on Foundations of Computational Science
8:30 am-2:45 pm 11/01/2019-08/31/2019 On August 29-31, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on Foundations of Computational Science. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by David Xianfeng Gu. Speakers: - Sarah Adel Bargal, Boston University
- Jianfeng Chen, Harvard
- Tat Seng Chua, National University of Singapore
- Ke Deng, Tsinghua
- David Xianfeng Gu, Stony Brook
- Yike Guo, Imperial College London
- Minlie Huang, Tsinghua
- Scott Kominers, Harvard
- Brian Kulis, Boston University
- Wee Sun Lee, National University of Singapore
- Qianxiao Li, National University of Singapore
- Hanzhong Liu, Tsinghua
- Jun Liu, Harvard
- Xiao-Li Meng, Harvard
- Cengiz Pehlevan, Harvard
- Donald Rubin, Harvard
- Suproteem Sarkar, Harvard
- Zuowei Shen, National University of Singapore
- Yuanchun Shi, Tsinghua
- Justin Solomon, MIT
- Hang Su, Tsinghua
- Maosong Sun, Tsinghua
- Mirac Suzgun, Harvard
- Sergiy Verstyuk, CMSA
- Xiaoqin Wang, Tsinghua
- Bin Xu, Tsinghua
- Jun Zhu, Tsinghua
- Wenwu Zhu, Tsinghua
Videos of the talks are contained in the Youtube playlist below. They can also be found through links in the schedule. - CMSA EVENT: Workshop on Aspects of General Relativity
8:30 am-3:30 pm 11/01/2019-05/26/2017 The Center of Mathematical Sciences and Applications will be hosting a workshop on General Relativity from May 23 – 24, 2016. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138. The workshop will start on Monday, May 23 at 9am and end on Tuesday, May 24 at 4pm. Speakers:- Po-Ning Chen, Columbia University
- Piotr T. Chruściel, University of Vienna
- Justin Corvino, Lafayette College
- Greg Galloway, University of Miami
- James Guillochon, Harvard University
- Lan-Hsuan Huang, University of Connecticut
- Dan Kapec, Harvard University
- Dan Lee, CUNY
- Alex Lupsasca, Harvard University
- Pengzi Miao, University of Miami
- Prahar Mitra, Harvard University
- Lorenzo Sironi, Harvard University
- Jared Speck, MIT
- Mu-Tao Wang, Columbia University
Please click Workshop Program for a downloadable schedule with talk abstracts.Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.Schedule:May 23 – Day 1 | 8:30am | Breakfast | 8:55am | Opening remarks | 9:00am – 9:45am | Greg Galloway, “Some remarks on photon spheres and their uniqueness“ | 9:45am – 10:30am | Prahar Mitra, “BMS supertranslations and Weinberg’s soft graviton theorem“ | 10:30am – 11:00am | Break | 11:00am – 11:45am | Dan Kapec, “Area, Entanglement Entropy and Supertranslations at Null Infinity“ | 11:45am – 12:30pm | Piotr T. Chruściel, “The cosmological constant and the energy of gravitational radiation” | 12:30pm – 2:00pm | Lunch | 2:00pm – 2:45pm | James Guillochon, “Tidal disruptions of stars by supermassive black holes: dynamics, light, and relics” | 2:45pm – 3:30pm | Mu-Tao Wang, “Quasi local conserved quantities in general relativity“ | 3:30pm – 4:00pm | Break | 4:00pm – 4:45pm | Po-Ning Chen, “Quasi local energy in presence of gravitational radiations” | 4:45pm – 5:30pm | Pengzi Miao, “Total mean curvature, scalar curvature, and a variational analog of Brown York mass“ | | May 24 – Day 2 | 8:45am | Breakfast | 9:00am – 9:45am | Justin Corvino, “Scalar curvature deformation and the Bartnik mass“ | 9:45am – 10:30am | Lan-Hsuan Huang, “Constraint Manifolds with the Dominant Energy Condition“ | 10:30am – 11:00am | Break | 11:00am – 11:45am | Dan Lee, “Lower semicontinuity of Huisken’s isoperimetric mass“ | 11:45am – 12:30pm | Jared Speck, “Shock Formation in Solutions to the Compressible Euler Equations“ | 12:30pm – 2:00pm | Lunch | 2:00pm – 2:45pm | Lorenzo Sironi, “Electron Heating and Acceleration in the Vicinity of Supermassive Black Holes“ | 2:45pm – 3:30pm | Alex Lupsasca, “Near Horizon Extreme Kerr Magnetospheres“ |
* Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Workshop on Aspects on General Relativity“.* This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.Organizers: Piotr T. Chruściel and Shing-Tung Yau - CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
8:30 am-2:00 pm 11/01/2019-10/24/2018 In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems. The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively? In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting. To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering). For example, in mathematics there are some beautiful links to Nash’s embedding theorem, connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution. In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied. The CMSA will be hosting a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA. The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida). For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Confirmed Speakers:- Arkhat Abzhanov, Imperial College
- Siobhan Braybrook, UCLA
- Cassandra Extavour, Harvard
- Anjali Goswami, University College London
- David Gu, Stony Brook
- Jukka Jernvall, Helsinki
- Eric Klassen, Florida State
- Sayan Mukherjee, Duke
- Peter Olver, U Minnesota
- Nipam Patel, Berkeley
- Stephanie Pierce, Harvard
- Karen Sears, UCLA
- Alain Trouve, ENS-Cachan, France
- Laurent Younes, Johns Hopkins
- CMSA EVENT: Morphogenesis: Geometry and Physics
8:30 am-2:30 pm 11/01/2019-12/05/2018 Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. So, how far are we from realizing the century-old vision that “Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed” ? To address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take, using the language of mathematics. In parallel, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution. In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems. The first workshop will focus on the interface between Morphometrics and Mathematics, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida). As part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Speakers:- Arkhat Abzhanov, Imperial College
- Yohanns Bellaiche, Paris
- Cheng Ming Chuong, USC
- Zev Gartner, UCSF
- Thomas Gregor, Princeton
- Dagmar Iber, Zurich
- Ian Jermyn, Durham University
- Raymond Keller, UVA
- Allon Klein, HMS
- Lisa Manning, Syracuse
- Cristina Marchetti, UCSB
- Sean Megason, HMS
- Elliot Meyerowitz, Caltech
- Michel Milinkovitch, Geneva
- Leonardo Morsut, USC
- Olivier Pourquié, HMS
- Eric Siggia, Rockefeller University
- Ben Simons, Cambridge
- Sebastian Streichan, UCSB
- Aryeh Warmflash, Rice
- CMSA EVENT: Geometric Analysis Approach to AI Workshop
8:30 am-5:30 pm 11/01/2019-01/21/2019 Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI. This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed. The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Speakers: - Sarah Adel Bargal, Boston University
- Guy Bresler, MIT
- Tina Eliassi-Rad, Northeastern
- Yun Raymond Fu, Northeastern
- Brian Kulis, Boston University
- Na Lei, Dalian University of Technology
- Yi Ma, UC Berkeley
- Minh Hoai Nguyen, Stony Brook
- Francesco Orabona, Boston University
- Cengiz Pehlevan, Harvard SEAS
- Tomaso Poggio, MIT
- Zhiwei Qin, DiDi Research America
- Kate Saenko, Boston University
- Dimitris Samaras, Stony Brook
- Johannes Schmidt-Hieber, University of Twente
- Steven Skiena, Stony Brook
- Vivienne Sze, MIT
- Naftali Tishby, ICNC
- Jiajun Wu, MIT
- Ying Nian Wu, UCLA
- Gangqiang Xia, Morgan Stanley
- Eric Xing, Carnegie Mellon
- Donghui Yan, UMass Dartmouth
- Alan Yuille, Johns Hopkins
- Juhua Zhu, Argus
- CMSA EVENT: 2019 Big Data Conference
8:30 am-4:40 pm 11/01/2019-08/20/2019 1 Oxford Street, Cambridge MA 02138 On August 19-20, 2019 the CMSA will be hosting our fifth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The talks will take place in Science Center Hall D, 1 Oxford Street. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants. Videos can be found in this Youtube playlist or in the schedule below. - CMSA EVENT: 2015 Conference on Big Data
8:45 am-4:00 pm 11/01/2019-10/26/2015 1 Oxford Street, Cambridge MA 02138 The Center of Mathematical Sciences and Applications will be having a conference on Big Data August 24-26, 2015, in Science Center Hall B at Harvard University. This conference will feature many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.For more info, please contact Sarah LaBauve at slabauve@math.harvard.edu. Registration for the conference is now closed.Please click here for a downloadable version of this schedule.Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found here. Monday, August 24 Time | Speaker | Title | 8:45am | Meet and Greet | | 9:00am | Sendhil Mullainathan | Prediction Problems in Social Science: Applications of Machine Learning to Policy and Behavioral Economics | 9:45am | Mike Luca | Designing Disclosure for the Digital Age | 10:30 | Break | | 10:45 | Jianqing Fan | Big Data Big Assumption: Spurious discoveries and endogeneity | 11:30am | Daniel Goroff | Privacy and Reproducibility in Data Science | 12:15pm | Break for Lunch | | 2:00pm | Ryan Adams | Exact Markov Chain Monte Carlo with Large Data | 2:45pm | David Dunson | Scalable Bayes: Simple algorithms with guarantees | 3:30pm | Break | | 3:45pm | Michael Jordan | Computational thinking, inferential thinking and Big Data | 4:30pm | Joel Tropp | Applied Random Matrix Theory | 5:15pm | David Woodruff | Input Sparsity and Hardness for Robust Subspace Approximation |
Tuesday, August 25 A Banquet from 7:00 – 8:30pm will follow Tuesday’s talks. This event is by invitation only. Wednesday, August 26 Time | Speaker | Title | 8:45am | Meet and Greet | | 9:00am | Ankur Moitra | Beyond Matrix Completion | 9:45am | Florent Krzakala | Optimal compressed sensing with spatial coupling and message passing | 10:30am | Break | | 10:45am | Piotr Indyk | Fast Algorithms for Structured Sparsity | 11:30am | Guido Imbens | Exact p-values for network inference | 12:15pm | Break for lunch | | 2:00pm | Edo Airoldi | Some fundamental ideas for causal inference on large networks | 2:45pm | Ronitt Rubinfeld | Something for almost nothing: sublinear time approximation algorithms | 3:30pm | Break | | 3:45pm | Lenka Zdeborova | Clustering of sparse networks: Phase transitions and optimal algorithms | 4:30pm | Jelani Nelson | Dimensionality reductions via sparse matrices |
- CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
9:00 am-1:30 pm 11/01/2019-02/09/2018 The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA. Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures. There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis. The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits. Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register. A list of lodging options convenient to the Center can also be found on our recommended lodgings page. Confirmed participants include: - Jozsef Balogh, University of Illinois, Urbana
- Fan Chung (Graham), University of California, San Diego
- Asaf Ferber, Massachusetts Institute of Technology
- Jacob Fox, Stanford Unviersity
- David Gamarnik, Massachusetts Institute of Technology
- Penny Haxell, University of Waterloo
- Hao Huang, Emory University
- Jeff Kahn, Rutgers University
- Peter Keevash, Oxford University
- Michael Krivelevich, Tel Aviv University
- Daniela Kühn, University of Birmingham
- Shoham Letzer, ITS Zürich
- Shachar Lovett, University of California, San Diego
- Eyal Lubetzky, Courant Institute
- Rob Morris, IMPA
- Bhargav Narayanan, Rutgers University
- Deryk Osthus, University of Birmingham
- Janos Pach, NYU
- Yuval Peres, Microsoft Redmond
- Alexey Pokryovskyi, ETH Zürich
- Wojciech Samotij, Tel Aviv University
- Lisa Sauermann, Stanford University
- Mathias Schacht, University of Hamburg
- Alexander Scott, University of Oxford
- Asaf Shapira, Tel Aviv University
- Jozef Skokan, London School of Economics
- Joel Spencer, New York University
- Angelika Steger, ETH Zurich
- Jacques Verstraete, University of California, San Diego
- Yufei Zhao, Massachusetts Institute of Technology
- David Zuckerman, University of Texas at Austin
Co-organizers of this workshop include Benny Sudakov and David Conlon. More details about this event, including participants, will be updated soon. - CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
9:00 am-5:00 pm 11/01/2019-05/08/2016 The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138 Organizers:D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau Speakers:- Netanel Blaier (MIT)
- Kwokwai Chan (CUHK)
- Bohan Fang (Peking University)
- Amanda Francis (BYU)
- Hansol Hong (CUHK)
- Heather Lee (Purdue University)
- Si Li (Tsinghua University)
- Yu-Shen Lin (Stanford University)
- Alex Perry (Harvard University)
- Hiro Tanaka (Harvard University)
- Sara Tukachinsky (HUJ)
- Michael Viscardi (MIT)
- Eric Zaslow (Northwestern University)
- Jingyu Zhao (Columbia University)
Please click here for the conference Main Website. Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.Schedule:May 6 – Day 1 | 9:00am | Breakfast | 9:35am | Opening remarks | 9:45am – 10:45am | Si Li, “Quantum master equation, chiral algebra, and integrability” | 10:45am – 11:15am | Break | 11:15am – 12:15pm | Sara Tukachinsky, “Point like bounding chains and open WDVV“ | 12:15pm – 1:45pm | Lunch | 1:45pm – 2:45pm | Bohan Fang, “Mirror B model for toric Calabi Yau 3 folds“ | 2:45pm – 3:00pm | Break | 3:00pm – 4:00pm | Hiro Tanaka, “Toward Fukaya categories over arbitrary coefficients“ | 4:00pm – 4:15pm | Break | 4:15pm – 5:15pm | Hansol Hong, “Noncommutative mirror functors“ | | May 7 – Day 2 | 9:00am | Breakfast | 9:45am – 10:45am | Eric Zaslow, “Lagrangian fillings what does the sheaf say?“ | 10:45am – 11:15am | Break | 11:15am – 12:15pm | Alex Perry, “Derived categories of Gushel Mukai varieties“ | 12:15pm – 1:45pm | Lunch | 1:45pm – 2:45pm | Amanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry“ | 2:45pm – 3:00pm | Break | 3:00pm – 4:00pm | Heather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions“ | 4:00pm – 4:15pm | Break | 4:15pm – 5:15pm | Yu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces“ | | May 8 – Day 3 | 9:00am | Breakfast | 9:45am – 10:45am | Kwokwai Chan, “HMS for local CY manifolds via SYZ“ | 10:45am – 11:15am | Break | 11:15am – 12:15pm | Netanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy“ | 12:15pm – 1:45pm | Lunch | 1:45pm – 2:45pm | Jingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration“ | 2:45pm – 3:00pm | Break | 3:00pm – 4:00pm | Michael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence“ |
This event is sponsored by the Simons Foundation and CMSA Harvard University. - CMSA EVENT: Workshop on Geometry, Imaging, and Computing
9:00 am-6:15 pm 11/01/2019-03/26/2018 - CMSA EVENT: Workshop on Optimization in Image Processing
9:00 am-12:30 pm 11/01/2019-06/30/2016 The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138. Titles, abstracts and schedule will be provided nearer to the event. Speakers:- Antonin Chambolle, CMAP, Ecole Polytechnique
- Raymond Chan, The Chinese University of Hong Kong
- Ke Chen, University of Liverpool
- Patrick Louis Combettes, Université Pierre et Marie Curie
- Mario Figueiredo, Instituto Superior Técnico
- Alfred Hero, University of Michigan
- Ronald Lok Ming Lui, The Chinese University of Hong Kong
- Mila Nikolova, Ecole Normale Superieure Cachan
- Shoham Sabach, Israel Institute of Technology
- Martin Benning, University of Cambridge
- Jin Keun Seo, Yonsei University
- Fiorella Sgallari, University of Bologna
- Gabriele Steidl, Kaiserslautern University of Technology
- Joachim Weickert, Saarland University
- Isao Yamada, Tokyo Institute of Technology
- Wotao Yin, UCLA
Please click Workshop Program for a downloadable schedule with talk abstracts.Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.
Schedule:June 27 – Day 1 | 9:00am | Breakfast | 9:20am | Opening remarks | 9:30am – 10:20am | Joachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems” | 10:20am – 10:50am | Break | 10:50am – 11:40pm | Patrick Louis Combettes, “Block-Iterative Asynchronous Variational Image Recovery” | 11:40am – 12:30pm | Isao Yamada, “Spicing up Convex Optimization for Certain Inverse Problems” | 12:30pm – 2:00pm | Lunch | 2:30pm – 3:20pm | Fiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization” | 3:20pm – 3:50pm | Break | 3:50pm – 4:40pm | Shoham Sabach, “A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems” | June 28 – Day 2 | 9:00am | Breakfast | 9:30am – 10:20am | Antonin Chambolle, “Acceleration of alternating minimisations” | 10:20am – 10:50am | Break | 10:50am – 11:40am | Mario Figueiredo, “ADMM in Image Restoration and Related Problems: Some History and Recent Advances” | 11:40am – 12:30pm | Ke Chen, “Image Restoration and Registration Based on Total Fractional-Order Variation Regularization” | 12:30pm – 2:30pm | Lunch | 2:30pm – 4:40pm | Discussions | June 29 – Day 3 | 9:00am | Breakfast | 9:30am – 10:20am | Alfred Hero, “Continuum relaxations for discrete optimization” | 10:20am – 10:50am | Break | 10:50am – 11:40am | Wotao Yin, “Coordinate Update Algorithms for Computational Imaging and Machine Learning” | 11:40am – 12:30pm | Mila Nikolova, “Limits on noise removal using log-likelihood and regularization” | 12:30pm – 2:30pm | Lunch | 2:30pm – 3:20pm | Martin Benning, “Nonlinear spectral decompositions and the inverse scale space method” | 3:20pm – 3:50pm | Break | 3:50pm – 4:40pm | Ronald Ming Lui, “TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification” | June 30 – Day 4 | 9:00am | Breakfast | 9:30am – 10:20am | Jin Keun Seo, “Mathematical methods for biomedical impedance imaging” | 10:20am – 10:50am | Break | 10:50am – 11:40am | Gabriele Steidl, “Iterative Multiplicative Filters for Data Labeling” | 11:40am – 12:30pm | Raymond Chan, “Point-spread function reconstruction in ground-based astronomy” |
* This event is sponsored by CMSA Harvard University.Organizers: Raymond Chan and Shing-Tung Yau - CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
9:00 am-11:55 am 11/01/2019-03/29/2019 The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. List of registrants Speakers:- Joan Bruna, Courant Institute
- Predrag Cvitanovic, Georgia Tech
- Stephan Hoyer, Google Research
- De Huang, Caltech
- George Karniadakis, Brown University
- Richard Kerswell, Cambridge University
- Stephane Mallat, ENS
- Stanley Osher, UCLA
- Jacob Page, Cambridge University
- Houman Owhadi, Caltech
- Zuowei Shen, National University of Singapore
- Jack Xin, UC Irvine
- Jinchao Xu, Penn State University
- Lexing Ying, Stanford University and Facebook AI Research
- Pengchuan Zhang, Microsoft Research
- CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
9:00 am-12:00 pm 11/01/2019-01/13/2017 The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. Please click here to register for this event. We have space for up to 30 registrants on a first come, first serve basis. We may be able to provide some financial support for grad students and postdocs interested in this event. If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com. Confirmed Participants: - CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
9:00 am-5:00 pm 11/01/2019-12/04/2016 The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138. The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years. The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields. Speakers:- Cliff Taubes (Harvard University)
- Valentino Tosatti (Northwestern University)
- Pengfei Guan (McGill University)
- Jared Speck (MIT)
Schedule:Please click Mini-School Program for a downloadable schedule with talk abstracts.Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.* This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University. - CMSA EVENT: Workshop on Coding and Information Theory
9:00 am-3:30 pm 11/01/2019-04/13/2018 The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA. This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems. Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory. One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program. Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities. Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics. All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration. Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register. Click here for a list of registrants. A list of lodging options convenient to the Center can also be found on our recommended lodgings page. Confirmed participants include: - Emmanuel Abbe, Princeton University
- Simeon Ball, Universitat Politècnica de Catalunya
- Boris Bukh, Carnegie Mellon University
- Mahdi Cheraghchi, Imperial College London
- Sivakanth Gopi, Princeton University
- Elena Grigorescu, University of Purdue
- Hamed Hassani, University of Pennsylvania
- Navin Kashyap, Indian Institute of Science
- Young-Han Kim, University of California, San Diego
- Swastik Kopparty, Rutgers University
- Nati Linial, Hebrew University of Jerusalem
- Shachar Lovett, University of California, San Diego
- William Martin, Worcester Polytechnic Institute
- Arya Mazumdar, University of Massachusetts at Amherst
- Or Meir, University of Haifa
- Olgica Milenkovic, ECE Illinois
- Chandra Nair, Chinese University of Hong Kong
- Yuval Peres, Microsoft Research
- Yury Polyanskiy, Massachusetts Institute of Technology
- Maxim Raginsky, University of Illinois at Urbana-Champaign
- Sankeerth Rao Karingula, UC San Diego
- Ankit Singh Rawat, MIT
- Noga Ron-Zewi, University of Haifa
- Ron Roth, Israel Institute of Technology
- Atri Rudra, State University of New York, Buffalo
- Alex Samorodnitsky, Hebrew University of Jerusalem
- Itzhak Tamo, Tel Aviv University
- Amnon Ta-Shma, Tel Aviv University
- Himanshu Tyagi, Indian Institute of Science
- David Zuckerman, University of Texas at Austin
- CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
9:15 am-3:25 pm 11/01/2019-09/11/2019 On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory. The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines. Topics include i) the classification of topological states ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii) interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems driven far from equlibrium v) quantum field theory approaches to topological matter. This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matter, and is the second of two workshops, in addition to a visitor program and seminars. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. Click here for a list of restaurants in the area. Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard) Partial list of speakers:- Nima Arkani-Hamed, IAS
- Jennifer Cano, Stony Brook
- Meng Cheng, Yale
- Lukasz Fidkowski, UW Seattle
- Daniel Freed, Texas
- Jeongwan Haah, Microsoft Research
- Anton Kapustin, Caltech
- Zohar Komargodski, SCGP/Stony Brook
- John McGreevy, UC San Diego
- Prineha Narang, Harvard
- Ying Ran, Boston College
- Shinsei Ryu, Chicago
- Cumrun Vafa, Harvard
- Chong Wang, Perimeter
- Zhenghan Wang, Microsoft Station Q
Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below. - CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
9:15 am-10:00 am 11/01/2019-04/17/2019 As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019. Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use. This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models. In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI). For a list of lodging options convenient to the Center, please visit our recommended lodgings page. List of registrants Tentative Speaker List: - Alessandro Achille, UCLA
- Vijay Balasubramanian, University of Pennsylvania
- Jeannette Bohg, Stanford
- Ed Connor, Johns Hopkins
- Moira Dillon, NYU
- Jacob Feldman, Rutgers
- Ila Fiete, MIT
- Sam Gershman, Harvard
- Gily Ginosar, Weizmann Institute of Science
- Lucia Jacobs, UC Berkeley
- Vivek Jayaraman, HHMI
- Talia Konkle, Harvard
- L. Mahadevan, Harvard
- Michael McCloskey, Johns Hopkins
- Sam Ocko, Stanford
- Peter Olver, University of Minnesota
- Anitha Pasupathy, University of Washington
- Sandro Romani, Janelia
- Stefano Soatto, UCLA
- Tatyana Sharpee, Salk Institute
- Dagmar Sternad, Northeastern
- Elizabeth Torres, Rutgers
Schedule:Monday, April 15 Time | Speaker | Title/Abstract | 8:30 – 9:00am | Breakfast | | 9:00 – 9:15am | Welcome and Introduction | | 9:15 – 10:00am | Vivek Jayaraman | Title: Insect cognition: Small tales of geometry & invariance Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena. | 10:00 – 10:45am | Elizabeth Torres | Title: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces. In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders. I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons. | 10:45 – 11:15am | Coffee Break | | 11:15 – 12:00pm | Peter Olver | Title: Symmetry and invariance in cognition — a mathematical perspective” Abstract: Symmetry recognition and appreciation is fundamental in human cognition. (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance. Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones. Mathematical prerequisites will be kept to a bare minimum. | 12:00 – 12:45pm | Stefano Soatto/Alessandro Achille | Title: Information in the Weights and Emergent Properties of Deep Neural Networks Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task. While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics. | 12:45 – 2:00pm | Lunch | | 2:00 – 2:45pm | Anitha Pasupathy | Title: Invariant and non-invariant representations in mid-level ventral visual cortex My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding. | 2:45 – 3:30pm | Jacob Feldman | Title: Bayesian skeleton estimation for shape representation and perceptual organization Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity. | 3:30 – 4:00pm | Tea Break | | 4:00 – 4:45pm | Moira Dillon | Title: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations. | 4:45 – 5:30pm | Michael McCloskey | Title: Axes and Coordinate Systems in Representing Object Shape and Orientation Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame. I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis? | 5:30 – 6:30pm | Reception | |
Tuesday, April 16 Time | Speaker | Title/Abstract | 8:30 – 9:00am | Breakfast | | 9:00 – 9:45am | Peter Olver | Title: Symmetry and invariance in cognition — a mathematical perspective” Abstract: Symmetry recognition and appreciation is fundamental in human cognition. (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance. Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones. Mathematical pre | 9:45 – 10:30am | Stefano Soatto/Alessandro Achille | Title: Information in the Weights and Emergent Properties of Deep Neural Networks Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task. While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics. | 10:30 – 11:00am | Coffee Break | | 11:00 – 11:45am | Jeannette Bohg | Title: On perceptual representations and how they interact with actions and physical representations Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data. | 11:45 – 12:30pm | Dagmar Sternad | Title: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system. | 12:30 – 2:00pm | Lunch | | 2:00 – 2:45pm | Sam Ocko | Title: Emergent Elasticity in the Neural Code for Space Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations. | 2:45 – 3:30pm | Tatyana Sharpee | Title: Hyperbolic geometry of the olfactory space Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes. | 3:30 – 4:00pm | Tea Break | | 4:00 – 4:45pm | Ed Connor | Title: Representation of solid geometry in object vision cortex Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality. | 4:45 – 5:30pm | L. Mahadevan | Title: Simple aspects of geometry and probability in perception Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context. |
Wednesday, April 17
Time | Speaker | Title/Abstract | 8:30 – 9:00am | Breakfast | | 9:00 – 9:45am | Gily Ginosar | Title: The 3D geometry of grid cells in flying bats Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice. Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1 (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel | 9:45 – 10:30am | Sandro Romani | Title: Neural networks for 3D rotations Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans. This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science). | 10:30 – 11:00am | Coffee Break | | 11:00 – 11:45am | Sam Gershman | Title: The hippocampus as a predictive map Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning. | 11:45 – 12:30pm | Lucia Jacobs | Title: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo. | 12:30 – 1:30pm | Lunch | | 1:30 – 2:15pm | Talia Konkle | Title: The shape of things and the organization of object-selective cortex Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry. | 2:15 – 3:00pm | Vijay Balasubramanian | Title: Becoming what you smell: adaptive sensing in the olfactory system Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors. In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors. The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules. I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors. The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain. The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans. It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb. | 3:00 – 3:45pm | Ila Feite | Title: Invariance, stability, geometry, and flexibility in spatial navigation circuits Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility. | 3:45 – 4:00pm | L Mahadevan – summary | |
- CMSA EVENT: The 2017 Charles River Lectures
9:15 am-5:30 pm 11/01/2019 The 2017 Charles River Lectures Charles River with Bench at Sunset Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community. The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University in the Harvard Science Center.
*************************************************** UPDATED LOCATIONHarvard University1 Oxford Street, Cambridge, MA 02138 (Map)Monday, October 2, 20179:15 AM – 5:30 PM************************************************** Please note that registration has closed. Speakers:Agenda:In Harvard Science Center Hall C: 8:45 am – 9:15 am: Coffee/light breakfast 9:15 am – 10:15 am: Ofer Zeitouni Title: Noise stability of the spectrum of large matrices Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory. The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood. 10:20 am – 11:20 am: Andrea Montanari Title: Algorithms for estimating low-rank matrices Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results. 11:20 am – 11:45 am: Break 11:45 am – 12:45 pm: Paul Bourgade Title: Random matrices, the Riemann zeta function and trees Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan. 1:00 pm – 2:30 pm: Lunch In Harvard Science Center Hall E: 2:45 pm – 3:45 pm: Roman Vershynin Title: Deviations of random matrices and applications Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science. 3:45 pm – 4:15 pm: Break 4:15 pm – 5:15 pm: Massimiliano Gubinelli Title: Weak universality and Singular SPDEs Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics. Poster:Organizers: Alexei Borodin, Henry Cohn, Vadim Gorin, Elchanan Mossel, Philippe Rigollet, Scott Sheffield, and H.T. Yau - CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
9:20 am-3:15 pm 11/01/2019-08/28/2018 On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines. This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter, and will be the first of two workshops, in addition to a visitor program and seminars. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. Speakers: - Zhen Bi, MIT
- Meng Cheng, Yale
- Dima Feldman, Brown
- Dominic Else, UCSB
- Liang Fu, MIT
- Fabian Grusdt, Harvard
- Ying Fei Gu, Harvard
- Bert Halperin, Harvard
- Anton Kapustin, Caltech
- Patrick Lee, MIT
- L. Mahadevan, Harvard
- Brad Marston, Brown
- Max Metlitski, MIT
- Emil V. Prodan, Yeshiva
- Achim Rosch, University of Cologne
- Mathias Scheurer, Harvard
- Marin Soljacic, MIT
- X. G. Wen, MIT
- Cenke Xu, UCSB
- Frank Zhang, Cornell
- Special Seminar
9:30 am-11:00 am 11/01/2019 - Seminars
9:30 am-10:30 am 11/01/2019 - CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
9:30 am-5:00 pm 11/01/2019-03/01/2019 From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS). This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm. The sessions will be held in \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\). - Special Seminar
- Seminars
9:50 am-10:50 am 11/01/2019 The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received. - Special Seminar
9:50 am-10:50 am 11/01/2019-04/26/2016 The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided. - Seminars
10:00 am-11:30 am 11/01/2019 - Seminars
10:00 am-11:30 am 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-12:00 am 11/01/2019-09/11/2018 - Seminars
10:30 am-11:42 am 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-12:40 pm 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
- Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-11:30 am 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Seminars
10:30 am-12:00 pm 11/01/2019 - Random Matrix & Probability Theory Seminar
10:32 am 11/01/2019 No additional detail for this event. - Special Seminar
10:36 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
10:38 am 11/01/2019 No additional detail for this event. - Special Seminar
10:42 am 11/01/2019 No additional detail for this event. - Seminars
10:43 am 11/01/2019 No additional detail for this event. - Random Matrix & Probability Theory Seminar
10:44 am 11/01/2019 No additional detail for this event. - Seminars
10:46 am 11/01/2019 No additional detail for this event. - Seminars
10:56 am 11/01/2019 No additional detail for this event. - Seminars
10:57 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
10:58 am 11/01/2019 No additional detail for this event. - General Relativity Seminar
- General Relativity Seminar
- Seminars
- Random Matrix & Probability Theory Seminar
11:00 am 11/01/2019 No additional detail for this event. - Seminars
11:00 am-11:00 pm 11/01/2019 - General Relativity Seminar
- General Relativity Seminar
- Seminars
- Seminars
- Seminars
11:00 am-12:00 am 11/01/2019-03/03/2018 - General Relativity Seminar
- Seminars
11:00 am-12:00 am 11/01/2019-04/14/2018 - Member Seminar
11:01 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
11:02 am 11/01/2019 No additional detail for this event. - Colloquium
11:03 am-11:04 am 11/01/2019 No additional detail for this event. - Random Matrix & Probability Theory Seminar
11:03 am 11/01/2019 No additional detail for this event. - Colloquium
11:04 am 11/01/2019 The CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10. Spring 2020Date | Speaker | Title/Abstract |
---|
1/29/2020 | David Yang (Harvard) | Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies. | 2/5/2020 | Scott Aaronson (UT Austin) Video | Title: Gentle Measurement of Quantum States and Differential Privacy Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography” of quantum states (that is, answering a large number of questions about a quantum state given few copies of it). Based on joint work with Guy Rothblum (arXiv:1904.08747) | 2/12/2020 | Scott Kominers (Harvard) | Title: A Compact, Logical Approach to Large-Market Analysis Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks. | 2/19/2020 | Peter Shor (MIT) | Title: Quantum Money from Lattices Abstract: Quantum money is a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure. | 2/26/2020 | Daneil Wise (McGill) | Title: The Cubical Route to Understanding Groups Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups. | 3/4/2020 4:45 – 5:45pm | Salil Vadhan (Harvard) | Title: Derandomizing Algorithms via Spectral Graph Theory Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage). In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved. | 3/11/2020 Postponed | Jose Scheinkman (Columbia) | This colloquium will be rescheduled at a later date. Title: Menu Costs and the Volatility of Inflation Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms. A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and can account for the positive relationship between inflation level and volatility that has been observed empirically. | 3/12/2020 4:00 – 5:00pm | Daniel Forger (University of Michigan) | This meeting will be taking place virtually on Zoom. Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance. Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists. | 3/25/2020 | Cancelled | | 4/1/2020 | Mauricio Santillana (Harvard) | This meeting will be taking place virtually on Zoom. Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs. | 4/8/2020 | Juven Wang (CMSA) | This meeting will be taking place virtually on Zoom. Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued) Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary explanation. We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in fundamental physics. Perhaps some of you (geometers, string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond | 4/15/2020 | Lars Andersson (Max-Planck Institute for Gravitational Physics) | This meeting will be taking place virtually on Zoom. Title: Stability of spacetimes with supersymmetric compactifications Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau. | 4/22/2020 | William Minicozzi (MIT) | This meeting will be taking place virtually on Zoom. Title: Mean curvature flow in high codimension Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow. Some of the ideas come from function theory on manifolds with Ricci curvature bounds. | 4/29/2020 | Gerhard Huisken (Tübingen University / MFO) | This meeting will be taking place virtually on Zoom. Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.) | 5/6/2020 | Lydia Bieri (UMich) | This meeting will be taking place virtually on Zoom. Title: Energy, Mass and Radiation in General Spacetimes Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity. | 5/13/2020 | Mikhail Lukin (Harvard) Video | This meeting will be taking place virtually on Zoom. Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays Abstract: We will discuss recent work at a new scientific interface between many-body physics and quantum information science. Specifically, we will describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays. Ongoing efforts to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed. | 5/20/2020 | | This meeting will be taking place virtually on Zoom. |
Fall 2019Date | Speaker | Title/Abstract |
---|
9/18/2019 | Bill Helton (UC San Diego) | Title: A taste of noncommutative convex algebraic geometry Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example, ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials. ◦ A convex NC semialgebraic set has a linear matrix inequality representation. ◦ The natural Nullstellensatz are falling into place. The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019. | 9/25/2019 | Pavel Etingof (MIT) | Title: Double affine Hecke algebras Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications. | 10/2/2019 | Spiro Karigiannis (University of Waterloo) | Title: Cohomologies on almost complex manifolds and their applications Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang. | 10/9/2019 | Hans Lindblad (Johns Hopkins University) | Title: Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition satisfy the preserved wave coordinate condition. Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times. John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition. Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition. Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields. Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity. | 10/16/2019 | Aram Harrow (MIT) Video | Title: Monogamy of entanglement and convex geometry Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems. | 10/23/2019 | No talk | | 10/30/2019 | Nima Arkani-Hamed (IAS) Video | Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity | 11/6/2019 | Kevin Costello (Perimeter Institute) Video | Title: A unified perspective on integrability Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics. I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu. | 11/13/2019 | Heather Harrington (University of Oxford) | Title: Algebra, Geometry and Topology of ERK Enzyme Kinetics Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman. | 11/20/2019 | Xi Yin (Harvard) Video | Title: An Introduction to the Non-Perturbative Bootstrap Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap | 11/25/2019 Monday | Madhu Sudan (Harvard) | Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits. In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction. Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard). | 12/4/2019 | Xiao-Gang Wen (MIT) Video | Title: Emergence of graviton-like excitations from a lattice model Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases. |
2018-2019Date | Speaker | Title/Abstract | 9/26/2018 | Xiao-Gang Wen (MIT) | Title: A classification of low dimensional topological orders and fully extended TQFTs Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs. | 10/03/2018 | Richard Schoen (Stanford) | Title: Perspectives on the scalar curvature Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied. | 10/10/2018 | Justin Solomon (MIT) | Title: Correspondence and Optimal Transport for Geometric Data Processing Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data. | 10/17/2018 | Jeremy England (MIT) | Title: Wisdom of the Jumble Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components. In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means. | 10/31/2018 | Moon Duchin (Tufts) | Title: Exploring the (massive) space of graph partitions Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts). I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics. | 11/14/2018 | Dusa McDuff (Columbia) | Title: The virtual fundamental class in symplectic geometry Abstract: Essential to many constructions and applications of symplectic geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim. | 11/19/2018 | Xiaoqin Wang (Johns Hopkins) | Title: Computational Principles of Auditory Cortex Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication. | 11/28/2018 | Robert Haslhofer (University of Toronto) | Title: Recent progress on mean curvature flow Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits. | 12/5/2018 | Robert McCann (University of Toronto) | Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics. Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf | 12/12/2018 | Zhiwei Yun (MIT) | Title: Shtukas: what and why Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them. | 1/30/2019 | Richard Freeman (Harvard) | Title: Innovation in Cell Phones in the US and China: Who Improves Technology Faster? Abstract: Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps. Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones. Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality. The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being. | 2/7/2019 *Thursday* | Ulrich Mueller (Princeton) | Title: Inference for the Mean Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap. | 2/13/2019 | Christian Santangelo (UMass Amherst) | Title: 4D printing with folding forms Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome. | 2/20/2019 | Michael Woodford (Columbia) | Title: Optimally Imprecise Memory and Biased Forecasts Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings. [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)] | 2/27/2019 2:30pm | Ian Martin (LSE) | Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou] | 3/6/2019 2:30pm | Philippe Sosoe (Cornell) | Title: A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation Abstract: In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors. (Joint work with Tadahiro Oh and Leonardo Tolomeo) | 3/13/2019 5:15pm | Greg Galloway (University of Miami) | Title: On the geometry and topology of initial data sets in General Relativity Abstract: A theme of long standing interest (to the speaker!) concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness). Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple. The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack. | 3/20/2019 | Sonia Jaffe (Microsoft) | Title: Quality Externalities on Platforms: The Case of Airbnb Abstract: We explore quality externalities on platforms: when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business. We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform. We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus. (Joint work with Peter Coles, Steven Levitt, and Igor Popov.) | 3/27/2019 5:15pm | Tatyana Sharpee (Salk Institute for Biological Studies) | Title: Hyperbolic geometry of the olfactory space. Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes. | 4/3/2019 2:30pm | Sarah Moshary (Chicago Booth) | Title: Deregulation through Direct Democracy: Lessons from Liquor Abstract: This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool. | 4/10/2019 2:30pm | Pietro Veronesi (Chicago Booth) | Title: Inequality Aversion, Populism, and the Backlash Against Globalization Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model. Paper Online Appendix | 4/17/2019 | Yi-Zhuang You (UCSD) | Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry. . [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103 [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804 [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223 | 4/24/2019 | Shengwu Li (Harvard) | Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism. |
Date………… | Speaker | Title | 02-09-2018 *Friday | Fan Chung (UCSD) | Sequences: random, structured or something in between There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems. | 02-14-2018 | Zhengwei Liu (Harvard Physics) | A new program on quantum subgroups Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing. | 02-21-2018 | Don Rubin (Harvard) | Essential concepts of causal inference — a remarkable history Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis. | 02-26-2018 *Monday | Tom Hou (Caltech) | Computer-assisted analysis of singularity formation of a regularized 3D Euler equation Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu. | 03-07-2018 | Richard Kenyon (Brown) | Harmonic functions and the chromatic polynomial Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam. | 03-14-2018 | | | 03-21-2018 | | | 03-28-2018 | Andrea Montanari (Stanford) | A Mean Field View of the Landscape of Two-Layers Neural Networks Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties? We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well. [Based on joint work with Song Mei and Phan-Minh Nguyen] | 03-30-2018 | | | 04-04-2018 | Ramesh Narayan (Harvard) | Black Holes and Naked Singularities Abstract: Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since, at least in the case of Black Holes, the Singularities are hidden inside the Event Horizon. However, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed, and some observational features of accretion flows in these spacetimes have been worked out. | 04-11-2018 | Pablo Parrilo (MIT) | Graph Structure in Polynomial Systems: Chordal Networks Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT). | 04-18-2018 | Washington Taylor (MIT) | On the fibration structure of known Calabi-Yau threefolds Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds. | 04-25-2018 | Xi Yin (Harvard) | How we can learn what we need to know about M-theory Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory. | 05-02-2018 | | | 05-09-2018 | | |
2016-2017Date | Name | Title/Abstract | 01-25-17 | Sam Gershman, Harvard Center for Brain Science, Department of Psychology | Title: Spectral graph theory of cognitive maps Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory. | 02-01-17 | Sean Eddy, Harvard Department of Molecular and Cellular Biology | Title: Biological sequence homology searches: the future of deciphering the past Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK. | 02-08-17 | Matthew Headrick, Brandeis University | Title: Quantum entanglement, classical gravity, and convex programming: New connections Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way. | 02-15-17 | Masahito Yamazaki, IMPU | Title: Geometry of 3-manifolds and Complex Chern-Simons Theory Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras. Video | 02-22-17 | Steven Rayan, University of Saskatchewan | Title: Higgs bundles and the Hitchin system Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics. As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence. From this point of view, the Hitchin map and spectral curves emerge. We’ll use these to form an impression of what the moduli space “looks like”. I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry. Video | 03-01-17 | Jun Liu, Harvard University | Title: Expansion of biological pathways by integrative Genomics Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays. Based on the joint work with Yang Li and the Vamsi Mootha lab. Video | 03-08-17 | Gabor Lippner, Northeastern University | Title: Evolution of cooperation in structured populations Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics. Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies. It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution. In this talk I will present new results about the model where the population is represented by an interaction network. We study the likelihood of a random mutation spreading through the entire population. The main question is to understand how the network influences this likelihood. After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks. | 03-15-17 | | Spring Break: No session | 03-22-17 | Gunther Uhlmann, University of Washington | Abstract: We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others. The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform. We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed. | 03-29-17 | Leslie Greengard, Courant Institute | Title: Inverse problems in acoustic scattering and cryo-electron microscopy Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy. NOTE: This talk will begin at 4:00pm | 04-05-17 | Gongjie Li, Harvard University | Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems. Video | 04-12-17 | Shlomo Razamat, Israel Institute of Technology | Title: Complicated four-dimensional physics and simple mathematics Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index, of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven. Video | 04-19-17 | Cumrun Vafa, Harvard University | Title: String Swampland Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography. | 04-27-17 | Mehran Kardar, MIT | Title: Levitation by Casimir forces in and out of equilibrium Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint. Note: This talk will begin at 3:00pm | 05-02-17 | Simona Cocco, Laboratoire de Physique Statistique de l’ENS | Title: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models have led to substantial progress in protein structural and functional predictions. Note: This talk will begin at 4:00pm | 05-03-17 | Xue-Mei Li, University of Warwick | Title: Perturbation to conservation law and stochastic averaging Abstract: A deterministic or random system with a conservation law is often used to approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces. Note: This talk will be held in the Science Center, Room 507 | 05-10-17 | | | 05-17-17 | Kwok Wai Chan, Chinese University of Hong Kong | Title: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations Abstract: In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015). | 05-24-17 | | NO COLLOQUIUM | 05-31-17 | Peter Michor, University of Vienna | Title: Geometry of shape spaces and diffeomorphism groups and some of their uses Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces. |
Date | Name | Title | 09-09-16 | Bong Lian, Brandeis | Title: Riemann-Hilbert Problem and Period Integrals Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems. | 09-14-16 | Sze-Man Ngai, Georgia Southern University | Title: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum. The asymptotic behavior of the eigenvalue counting function for the associated Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results. | 09-21-16 | Prof. L. Mahadevan, Harvard SEAS | Title: “Morphogenesis: Biology, Physics and Mathematics” Abstract: A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology. Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains. I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology. | 09-28-16 | Hong Liu, MIT | Title: A new theory of fluctuating hydrodynamics Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate for capturing fluctuations. In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure. We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular, the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations. Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry. | 10-05-16 | Alexander Logunov, Tel-Aviv University | Title: Zeroes of harmonic functions and Laplace eigenfunctions Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete. | 10-12-16 | Conan Nai Chung Leung, CUHK | Title: Coisotropic A-branes and their SYZ transform Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.” | 10-19-16 | Vaughan Jones, UC Berkeley | Title: Are the Thompson groups any good as a model for Diff(S^1)? Abstract. The Thompson groups are by definition groups of piecewise linear diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can be conjugated to a group of smooth diffeomorphisms. That’s the good news. The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any procedure analogous to the constructions of the central extension of Diff(S^1)? I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it. | 10-26-16 | Henry Cohn, Microsoft | Sums of squares, correlation functions, and exceptional geometric structures Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding. How can we understand and prove their optimality? In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems. | 11-02-16 | Christian Borgs, Microsoft | Title: Graphon processes and limits of sparse graph sequences Abstract: The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs. Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection. While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model. In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits. The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life. | 11-09-16 TIME CHANGE: 4PM | Norden E. Huang, National Central University, (Taiwan) | Title: On Holo-Hilbert Spectral Analysis Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation. | 11-16-16 | Tristan Collins, Harvard University TIME CHANGE: 3:30PM | Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow Abstract: I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow. This is joint work with Valentino Tosatti. | 11-22-16 TUESDAY TIME CHANGE: 4-5PM | Xiangfeng Gu, Stonybrook | Title: Differential Geometric Methods for Engineering Applications Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation. | 11-30-16 TIME CHANGE: 4:20PM | Sharad Ramanathan, Harvard MCB & SEAS | Title: Finding co-ordinate systems to monitor the development of mammalian embryos | 12-07-16 | Valentino Tosatti, Northwestern | Title: Metric limits of hyperkahler manifolds Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang. | 12-14-16 | | |
2015-2016Date | Name | Title | 09-02-2015 | Madhu Sudan | Robust low-degree testing | 09-09-2015 | Mithat Unsal
| What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles | 09-16-2015 | Subir Sachdev | Bekenstein-Hawking entropy and strange metals | 09-23-2015 | Felix Finster | Linear hyperbolic equations in a rotating black hole geometry | 09-30-2015 | Leslie Valiant | Holographic Algorithms | 10-07-2015 | Christopher Rogan | Exploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond | 10-14-2015 | Boaz Barak, Harvard SEAS | Convexity, Bayesianism, and the quest towards Optimal Algorithms | 10-21-2015 | Zhouping Xin | Entropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems | 10-28-2015 | Cristopher Moore | Statistical inference, statistical physics, and the community detection problem | 11-04-2015 | Tom Hou | Blowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations | 11-11-2015 | Stan Osher, UCLA | Overcoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere | 11-18-2015 | Xiaole Shirley Liu | Inference of transcriptional regulation in cancers | 11-25-2015 | Thanksgiving | No seminar | 12-02-2015 | Scott Kominers | Generalized Matching Market Design: Theory and Practice | 12-09-2015 | Matthew Holman | Dynamical Chaos in Kepler Planetary Systems | 01-27-2016 | Conan Leung | Some modern aspects of Morse theory | 02-03-2016 | Camillo De Lellis | From Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence | 02-10-2016 | Chun Peng Wang | | 02-17-2016 | Samuel Kou, Harvard Statistics | Big data, Google and disease detection: the statistical story | 02-24-2016 | Dan Xie, Harvard CMSA | Singularity theory and supersymmetric field theory | 03-02-2016 | Lydia Bieri | Mathematical General Relativity | 03-09-2016 | Piotr Chrusciel | The mathematics of gravitation | 03-16-2016 | Spring Break | No Talk | 03-23-2016 | Richard Freeman, Harvard Economics | Pulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity. | 03-30-2016 | David Garfinkel, Oakland University | Gravitational Wave Memory | 04-04-2016 (Hall A, Science Center) | Xianfeng David Gu, Stony Brook University | A Discrete Variational Approach for Solving Monge-Ampere Equation | 04-06-2016 | Lars Hernquist, Harvard | Next Generation Cosmological Simulations: Galaxy Assembly and Evolution | 04-13-2016 | Jun Zhang, Univ. of Michigan-Ann Arbor | Kahler and Para-Kahler Structure in Information Geometry | 04-20-2016 | Sijue Wu, Univ. of Michigan | On two dimensional gravity water waves with angled crests | 04-27-2016 | Paul Seidel, MIT | Topological quantum field theory and the Gauss-Manin connection | 05-04-2016 | Hirosi Ooguri, Caltech | String Theory And Its Applications in Mathematics and Physics | 05-11-2016 (4pm – 5pm) | Juerg Froehlich, ETH and IAS | Implications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space |
- Colloquium
11:05 am-11:06 am 11/01/2019 No additional detail for this event. - Colloquium
11:07 am-11:08 am 11/01/2019 No additional detail for this event. - Colloquium
11:08 am-11:09 am 11/01/2019 No additional detail for this event. - Random Matrix & Probability Theory Seminar
11:12 am 11/01/2019 No additional detail for this event. - Random Matrix & Probability Theory Seminar
11:16 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
11:17 am 11/01/2019 No additional detail for this event. - Colloquium
11:21 am-11:22 am 11/01/2019 No additional detail for this event. - Seminars
11:21 am 11/01/2019 No additional detail for this event. - Random Matrix & Probability Theory Seminar
11:22 am 11/01/2019 No additional detail for this event. - Special Seminar
11:24 am 11/01/2019 No additional detail for this event. - Special Seminar
11:25 am 11/01/2019 No additional detail for this event. - CMSA EVENT: Learning from health data in the million genome era
11:26 am 11/01/2019 On November 1, 2019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page. Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system. Speakers: - Heidi Rehm, Ph.D.
Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform. - Saiju Pyarajan, Ph.D.
Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS - Tianxi Cai, Sci.D
John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health - Susan Redline, M.D., M.P.H
Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center - Avinash Sahu, Ph.D.
Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health - Peter J. Park, Ph.D.
Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School - David Roberson
Community Engagement Manager, Seven Bridges
- Seminars
11:30 am-12:00 pm 11/01/2019 - Mathematical Physics Seminar
11:30 am 11/01/2019 No additional detail for this event. - Seminars
11:32 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
11:33 am 11/01/2019 No additional detail for this event. - Mathematical Physics Seminar
11:34 am 11/01/2019 No additional detail for this event. - Special Seminar
11:35 am 11/01/2019 No additional detail for this event. - CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
11:36 am 11/01/2019-10/30/2019 - Member Seminar
11:37 am 11/01/2019 Hansol Hong, Harvard Title: Homological Mirror Functors Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold. We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction. - Colloquium
11:39 am-11:40 am 11/01/2019 No additional detail for this event. - Colloquium
11:40 am-11:41 am 11/01/2019 No additional detail for this event. - Seminars
11:42 am 11/01/2019 No additional detail for this event. - Colloquium
11:43 am 11/01/2019 No additional detail for this event. - Colloquium
11:45 am 11/01/2019 No additional detail for this event. - Seminars
|