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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190225T093000
DTEND;TZID=America/New_York:20190301T170000
DTSTAMP:20260506T034556
CREATED:20230715T090551Z
LAST-MODIFIED:20240209T214453Z
UID:10000108-1551087000-1551459600@cmsa.fas.harvard.edu
SUMMARY:Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
DESCRIPTION: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.  \nKey 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.\nThe sessions will be held in  \(G02\) (downstairs) at 20 Garden\, except for Tuesday afternoon\, when the talk will be in \(G10\).
URL:https://cmsa.fas.harvard.edu/event/growth-and-zero-sets-of-eigenfunctions-and-of-solutions-to-elliptic-partial-differential-equations/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190220T163000
DTEND;TZID=America/New_York:20190220T173000
DTSTAMP:20260506T034556
CREATED:20240212T114533Z
LAST-MODIFIED:20240514T182813Z
UID:10002102-1550680200-1550683800@cmsa.fas.harvard.edu
SUMMARY:Optimally Imprecise Memory and Biased Forecasts
DESCRIPTION:Speaker: Michael Woodford (Columbia) \nTitle: Optimally Imprecise Memory and Biased Forecasts \nAbstract: 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. [Joint work with Rava Azeredo da Silveira and Yeji Sung
URL:https://cmsa.fas.harvard.edu/event/2-20-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022019-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190207T163000
DTEND;TZID=America/New_York:20190207T173000
DTSTAMP:20260506T034556
CREATED:20240212T101329Z
LAST-MODIFIED:20240514T182948Z
UID:10001963-1549557000-1549560600@cmsa.fas.harvard.edu
SUMMARY:Inference for the Mean
DESCRIPTION:Speaker: Ulrich Mueller (Princeton) \nTitle: Inference for the Mean \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/2-7-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-020719.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190119T163000
DTEND;TZID=America/New_York:20190119T163000
DTSTAMP:20260506T034556
CREATED:20240212T100703Z
LAST-MODIFIED:20240514T183205Z
UID:10001956-1547915400-1547915400@cmsa.fas.harvard.edu
SUMMARY:Innovation in Cell Phones in the US and China: Who Improves Technology Faster?
DESCRIPTION:Speaker: Richard B. Freeman (Harvard University and NBER) \nTitle: Innovation in Cell Phones in the US and China: Who Improves Technology Faster? \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/1-30-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Screen-Shot-2019-01-29-at-9.16.13-AM.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190118T083000
DTEND;TZID=America/New_York:20190121T173000
DTSTAMP:20260506T034556
CREATED:20230715T090318Z
LAST-MODIFIED:20241212T192232Z
UID:10000105-1547800200-1548091800@cmsa.fas.harvard.edu
SUMMARY:Geometric Analysis Approach to AI Workshop
DESCRIPTION: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.\nOn January 18-21\, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI. \nThis 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. \nThe 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. \nThe workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA.  \nSpeakers:  \n\nSarah Adel Bargal\, Boston University\nGuy Bresler\, MIT\nTina Eliassi-Rad\, Northeastern\nYun Raymond Fu\, Northeastern\nBrian Kulis\, Boston University\nNa Lei\, Dalian University of Technology\nYi Ma\, UC Berkeley\nMinh Hoai Nguyen\, Stony Brook\nFrancesco Orabona\, Boston University\nCengiz Pehlevan\, Harvard SEAS\nTomaso Poggio\, MIT\nZhiwei Qin\, DiDi Research America\nKate Saenko\, Boston University\nDimitris Samaras\, Stony Brook\nJohannes Schmidt-Hieber\, University of Twente\nSteven Skiena\, Stony Brook\nVivienne Sze\, MIT\nNaftali Tishby\, ICNC\nJiajun Wu\, MIT\nYing Nian Wu\, UCLA\nGangqiang Xia\, Morgan Stanley\nEric Xing\, Carnegie Mellon\nDonghui Yan\, UMass Dartmouth\nAlan Yuille\, Johns Hopkins\nJuhua Zhu\,  Argus
URL:https://cmsa.fas.harvard.edu/event/geometric-analysis-approach-to-ai-workshop/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Geo-Analysis-Poster-final-e1547584167900.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181205T163000
DTEND;TZID=America/New_York:20181205T173000
DTSTAMP:20260506T034556
CREATED:20240213T072513Z
LAST-MODIFIED:20240514T183912Z
UID:10002179-1544027400-1544031000@cmsa.fas.harvard.edu
SUMMARY:Displacement convexity of Boltzmann's entropy characterizes positive energy in general relativity
DESCRIPTION:Speaker: Robert McCann (University of Toronto) \nTitle: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity \nAbstract: 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 \n 
URL:https://cmsa.fas.harvard.edu/event/12-05-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-120518.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181203T083000
DTEND;TZID=America/New_York:20181205T143000
DTSTAMP:20260506T034556
CREATED:20230715T090021Z
LAST-MODIFIED:20250305T212541Z
UID:10000103-1543825800-1544020200@cmsa.fas.harvard.edu
SUMMARY:Morphogenesis: Geometry and Physics
DESCRIPTION: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 ?” \nTo 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. \nIn 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.\nThe 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). \nAs 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. \nVideos\nSpeakers:\n\nArkhat Abzhanov\, Imperial College\nYohanns Bellaiche\, Paris\nCheng Ming Chuong\, USC\nZev Gartner\, UCSF\nThomas Gregor\, Princeton\nDagmar Iber\, Zurich\nIan Jermyn\, Durham University\nRaymond Keller\, UVA\nAllon Klein\, HMS\nLisa Manning\, Syracuse\nCristina Marchetti\, UCSB\nSean Megason\, HMS\nElliot Meyerowitz\, Caltech\nMichel Milinkovitch\, Geneva\nLeonardo Morsut\, USC\nOlivier Pourquié\, HMS\nEric Siggia\, Rockefeller University\nBen Simons\, Cambridge\nSebastian Streichan\, UCSB\nAryeh Warmflash\, Rice
URL:https://cmsa.fas.harvard.edu/event/morphogenesis-geometry-and-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181128T163000
DTEND;TZID=America/New_York:20181128T173000
DTSTAMP:20260506T034556
CREATED:20240213T072819Z
LAST-MODIFIED:20240514T184301Z
UID:10002180-1543422600-1543426200@cmsa.fas.harvard.edu
SUMMARY:Recent progress on mean curvature flow
DESCRIPTION:Speaker: Robert Haslhofer (University of Toronto) \nTitle: Recent progress on mean curvature flow \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/11-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-112818-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181119T150000
DTEND;TZID=America/New_York:20181119T160000
DTSTAMP:20260506T034556
CREATED:20240213T071141Z
LAST-MODIFIED:20240514T184752Z
UID:10002165-1542639600-1542643200@cmsa.fas.harvard.edu
SUMMARY:Computational Principles of Auditory Cortex
DESCRIPTION:Speaker: Xiaoqin Wang (Johns Hopkins University) \nTitle: Computational Principles of Auditory Cortex \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/11-19-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111918.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181114T160000
DTEND;TZID=America/New_York:20181114T170000
DTSTAMP:20260506T034556
CREATED:20240213T071016Z
LAST-MODIFIED:20240514T184520Z
UID:10002163-1542211200-1542214800@cmsa.fas.harvard.edu
SUMMARY:The virtual fundamental class in symplectic geometry
DESCRIPTION:Speaker: Dusa McDuff (Columbia University)  \nTitle: The virtual fundamental class in symplectic geometry \nAbstract: 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. \n 
URL:https://cmsa.fas.harvard.edu/event/11-14-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111418.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181031T163000
DTEND;TZID=America/New_York:20181031T173000
DTSTAMP:20260506T034556
CREATED:20240213T072029Z
LAST-MODIFIED:20240514T184941Z
UID:10002176-1541003400-1541007000@cmsa.fas.harvard.edu
SUMMARY:Exploring the (massive) space of graph partitions
DESCRIPTION:Speaker: Moon Duchin (Tufts) \nTitle: Exploring the (massive) space of graph partitions \nAbstract: 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. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-10-31-2018/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_10_29_11_55_54.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181022T090000
DTEND;TZID=America/New_York:20190417T170000
DTSTAMP:20260506T034556
CREATED:20230904T082647Z
LAST-MODIFIED:20240105T154957Z
UID:10000009-1540198800-1555520400@cmsa.fas.harvard.edu
SUMMARY:Mathematical Biology
DESCRIPTION:During Academic year 2018-19\, the CMSA will be hosting a Program on Mathematical Biology. \nJust over a century ago\, the biologist\, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. \nIn 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. And in mathematics and computation\, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry\, statistics and inference.  So\, how far are we from realizing a descriptive\, predictive and controllable theory of biological shape? \nIn 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 \nThe CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics\, Morphogenesis and Mathematics will take place on October 22-26.  \nA workshop on Morphogenesis: Geometry and Physics will take place on December 3-6\, 2018. \nA workshop on Invariance and Geometry in Sensation\, Action and Cognition will take place on April 15-17\, 2019.
URL:https://cmsa.fas.harvard.edu/event/mathematical-biology/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181022T083000
DTEND;TZID=America/New_York:20181024T140000
DTSTAMP:20260506T034556
CREATED:20230715T084844Z
LAST-MODIFIED:20250305T212456Z
UID:10000099-1540197000-1540389600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Morphometrics\, Morphogenesis and Mathematics
DESCRIPTION: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. \nThe 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? \nIn 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. \nTo understand these questions\, we need to describe shape (biomathematics)\, predict shape (biophysics)\, and design shape (bioengineering). \nFor 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. \nIn 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. \nThe CMSA will be hosting a Workshop on Morphometrics\, Morphogenesis and Mathematics from October 22-24\, 2018 at the Center of Mathematical Sciences and Applications\, located at 20 Garden Street\, Cambridge\, MA. \nThe workshop is organized by L. Mahadevan (Harvard)\, O. Pourquie (Harvard)\, A. Srivastava (Florida). \nVideos of the talks\nConfirmed Speakers:\n\nArkhat Abzhanov\, Imperial College\nSiobhan Braybrook\, UCLA\nCassandra Extavour\, Harvard\nAnjali Goswami\, University College London\nDavid Gu\, Stony Brook\nJukka Jernvall\, Helsinki\nEric Klassen\, Florida State\nSayan Mukherjee\, Duke\nPeter Olver\, U Minnesota\nNipam Patel\, Berkeley\nStephanie Pierce\, Harvard\nKaren Sears\, UCLA\nAlain Trouve\, ENS-Cachan\, France\nLaurent Younes\, Johns Hopkins
URL:https://cmsa.fas.harvard.edu/event/workshop-on-morphometrics-morphogenesis-and-mathematics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180929T083000
DTEND;TZID=America/New_York:20180930T150000
DTSTAMP:20260506T034556
CREATED:20230715T084506Z
LAST-MODIFIED:20250328T145116Z
UID:10000090-1538209800-1538319600@cmsa.fas.harvard.edu
SUMMARY:F-Theory Workshop
DESCRIPTION:The CMSA hosted an F-Theory workshop September 29-30\, 2018. The workshop was held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \nYoutube Playlist  \nOrganizers: \n\nPaolo Aluffi (Florida State)\nLara B. Anderson (Virginia Tech)\nMboyo Esole (Northeastern)\nShing-Tung Yau (Harvard)\n\nSpeakers: \n\nMirjam Cvetic\, University of Pennsylvania\nTommaso de Fernex\, University of Utah\nJames Gray\, Virginia Tech\nJonathan Heckman\, University of Pennsylvania\nMonica Kang\, Harvard University\nSándor Kovács\, University of Washington\nAnatoly Libgober\, UIC\nMatilde Marcolli\, Caltech\, University of Toronto\, and Perimeter Institute\nWashington Taylor\, MIT\nCumrun Vafa\, Harvard University
URL:https://cmsa.fas.harvard.edu/event/f-theory-conference/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180827T092000
DTEND;TZID=America/New_York:20180828T151500
DTSTAMP:20260506T034556
CREATED:20230715T084116Z
LAST-MODIFIED:20250305T184118Z
UID:10000089-1535361600-1535469300@cmsa.fas.harvard.edu
SUMMARY:Kickoff Workshop on Topology and Quantum Phases of Matter
DESCRIPTION: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. \nThis 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. \nThe workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \nSpeakers:  \n\nZhen Bi\, MIT\nMeng Cheng\, Yale\nDima Feldman\, Brown\nDominic Else\, UCSB\nLiang Fu\, MIT\nFabian Grusdt\, Harvard\nYing Fei Gu\, Harvard\nBert Halperin\, Harvard\nAnton Kapustin\, Caltech\nPatrick Lee\, MIT\nL. Mahadevan\, Harvard\nBrad Marston\, Brown\nMax Metlitski\, MIT\nEmil V. Prodan\, Yeshiva\nAchim Rosch\, University of Cologne\nMathias Scheurer\, Harvard\nMarin Soljacic\, MIT\nX. G. Wen\, MIT\nCenke Xu\, UCSB\nFrank Zhang\, Cornell
URL:https://cmsa.fas.harvard.edu/event/kickoff-workshop-on-topology-and-quantum-phases-of-matter/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Topological-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180413T163000
DTEND;TZID=America/New_York:20180413T173000
DTSTAMP:20260506T034556
CREATED:20240213T065558Z
LAST-MODIFIED:20240514T185400Z
UID:10002143-1523637000-1523640600@cmsa.fas.harvard.edu
SUMMARY:On the fibration structure of known Calabi-Yau threefolds
DESCRIPTION:Speaker: Washington Tayor (MIT) \nTitle: On the fibration structure of known Calabi-Yau threefolds \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/4-18-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_04_13_11_01_32-e1523633302205.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180411T163000
DTEND;TZID=America/New_York:20180411T173000
DTSTAMP:20260506T034556
CREATED:20240213T065052Z
LAST-MODIFIED:20240515T144439Z
UID:10002134-1523464200-1523467800@cmsa.fas.harvard.edu
SUMMARY:Graph Structure in Polynomial Systems: Chordal Networks
DESCRIPTION:Speaker: Pablo Parillo (MIT) \nTitle: Graph Structure in Polynomial Systems: Chordal Networks \nAbstract: 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).
URL:https://cmsa.fas.harvard.edu/event/4-11-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_04_10_09_58_15-e1523369654177.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180409T090000
DTEND;TZID=America/New_York:20180413T153000
DTSTAMP:20260506T034556
CREATED:20230717T175359Z
LAST-MODIFIED:20250305T214334Z
UID:10000079-1523264400-1523633400@cmsa.fas.harvard.edu
SUMMARY:Workshop on Coding and Information Theory
DESCRIPTION: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. \nThis 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. \nSquarely 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. \nParticipation: The workshop is open to participation by all interested researchers\, subject to capacity. \nA list of lodging options convenient to the Center can also be found on our recommended lodgings page. \nConfirmed participants include: \n\nEmmanuel Abbe\, Princeton University\nSimeon Ball\, Universitat Politècnica de Catalunya\nBoris Bukh\, Carnegie Mellon University\nMahdi Cheraghchi\, Imperial College London\nSivakanth Gopi\, Princeton University\nElena Grigorescu\, University of Purdue\nHamed Hassani\, University of Pennsylvania\nNavin Kashyap\, Indian Institute of Science\nYoung-Han Kim\, University of California\, San Diego\nSwastik Kopparty\, Rutgers University\nNati Linial\, Hebrew University of Jerusalem\nShachar Lovett\, University of California\, San Diego\nWilliam Martin\, Worcester Polytechnic Institute\nArya Mazumdar\, University of Massachusetts at Amherst\nOr Meir\, University of Haifa\nOlgica Milenkovic\, ECE Illinois\nChandra Nair\, Chinese University of Hong Kong\nYuval Peres\, Microsoft Research\nYury Polyanskiy\, Massachusetts Institute of Technology\nMaxim Raginsky\, University of Illinois at Urbana-Champaign\nSankeerth Rao Karingula\, UC San Diego\nAnkit Singh Rawat\, MIT\nNoga Ron-Zewi\, University of Haifa\nRon Roth\, Israel Institute of Technology\nAtri Rudra\, State University of New York\, Buffalo\nAlex Samorodnitsky\, Hebrew University of Jerusalem\nItzhak Tamo\, Tel Aviv University\nAmnon Ta-Shma\, Tel Aviv University\nHimanshu Tyagi\, Indian Institute of Science\nDavid Zuckerman\, University of Texas at Austin
URL:https://cmsa.fas.harvard.edu/event/workshop-on-coding-and-information-theory/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180405T090000
DTEND;TZID=America/New_York:20180407T170000
DTSTAMP:20260506T034556
CREATED:20230717T175058Z
LAST-MODIFIED:20250304T212649Z
UID:10000078-1522918800-1523120400@cmsa.fas.harvard.edu
SUMMARY:Simons Collaboration Workshop\, April 5-7\, 2018
DESCRIPTION:The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7\, 2018. The workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \nPlease click here to register for this event.  We have space for up to 30 registrants on a first come\, first serve basis. \nWe 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. \nConfirmed Speakers: \n\nJacob Bourjaily (Niels Bohr Institute)\nMandy Cheung (Havard University)\nTristan Collins (Harvard University)\nYoosik Kim (Boston University)\nYu-Shen Lin (Harvard University)\nCheuk-Yu Mak (Cambridge University)\nYu Pan (MIT)\nMauricio Romo (Tsinghua University)\nShu-Heng Shao (IAS)\nZack Sylvan (Columbia University)\nDmitry Vaintrob (IAS)
URL:https://cmsa.fas.harvard.edu/event/simons-collaboration-workshop-april-5-7-2018/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Amplituhedron-0c.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180404T163000
DTEND;TZID=America/New_York:20180404T163000
DTSTAMP:20260506T034556
CREATED:20240213T064751Z
LAST-MODIFIED:20240515T174223Z
UID:10002129-1522859400-1522859400@cmsa.fas.harvard.edu
SUMMARY:Black Holes and Naked Singularities
DESCRIPTION:Speaker: Ramesh Narayan\, Department of Astronomy\, Harvard University \nTitle: Black Holes and Naked Singularities \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/4-4-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-040418-e1522340269661.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180328T163000
DTEND;TZID=America/New_York:20180328T173000
DTSTAMP:20260506T034556
CREATED:20240213T064501Z
LAST-MODIFIED:20240515T174531Z
UID:10002125-1522254600-1522258200@cmsa.fas.harvard.edu
SUMMARY:A Mean Field View of the Landscape of Two-Layers Neural Networks
DESCRIPTION:Speaker: Andrea Montanari (Stanford) \nTitle: A Mean Field View of the Landscape of Two-Layers Neural Networks \nAbstract: 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]
URL:https://cmsa.fas.harvard.edu/event/3-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-032818-e1521831836462-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180324T090000
DTEND;TZID=America/New_York:20180326T181500
DTSTAMP:20260506T034556
CREATED:20230717T174646Z
LAST-MODIFIED:20250304T212149Z
UID:10000074-1521882000-1522088100@cmsa.fas.harvard.edu
SUMMARY:Workshop on Geometry\, Imaging\, and Computing
DESCRIPTION:On March 24-26\, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry\, Imaging\, and Computing\, based off  the journal of the same name. The workshop will take place in CMSA building\, G10. \nThe organizing committee consists of Yang Wang (HKUST)\, Ronald Lui (CUHK)\, David Gu (Stony Brook)\, and Shing-Tung Yau (Harvard). \nConfirmed Speakers: \n\nJianfeng Cai (HKUST)\nShikui Chen (Stony Brook)\nJerome Darbon (Brown University)\nLaurent Demanet (MIT)\nDavid Gu (Stony Brook)\nMonica Hurdal (Florida State University)\nRongjie Lai (RPI)\nYue Lu (Harvard)\nRonald Lok Ming Lui (CUHK)\nLakshminarayanan Mahadevan (Harvard)\nEric Miller (Tufts)\nAshley Prater  (AFOSR)\nLixin Shen (Syracuse University)\nAllen Tannenbaum (Stony Brook)\nGuowei Wei (Michigan State)\nStephen Wong (Houston Methodist)\nJun Zhang (University of Michigan\, Ann Arbor)\nSong Zhang (Purdue University)\nHongkai Zhao (University of California\, Irvine)
URL:https://cmsa.fas.harvard.edu/event/workshop-on-geometry-imaging-and-computing/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GIC-Poster-2-e1520002551865.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180221T163000
DTEND;TZID=America/New_York:20180221T173000
DTSTAMP:20260506T034556
CREATED:20240213T063335Z
LAST-MODIFIED:20240515T175648Z
UID:10002115-1519230600-1519234200@cmsa.fas.harvard.edu
SUMMARY:Essential concepts of Causal inference—a remarkable history
DESCRIPTION:Speaker: Don Rubin (Harvard Statistics) \nTitle: Essential concepts of Causal inference—a remarkable history \nAbstract: 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. \n 
URL:https://cmsa.fas.harvard.edu/event/2-21-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022118-e1518810758992.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180205T090000
DTEND;TZID=America/New_York:20180209T170000
DTSTAMP:20260506T034556
CREATED:20230717T174149Z
LAST-MODIFIED:20250304T211916Z
UID:10000044-1517821200-1518195600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Probabilistic and Extremal Combinatorics
DESCRIPTION: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. \nExtremal 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. \nThere 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. \nThe 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. \nParticipation: The workshop is open to participation by all interested researchers\, subject to capacity. \nConfirmed participants include: \n\nJozsef Balogh\, University of Illinois\, Urbana\nFan Chung (Graham)\, University of California\, San Diego\nAsaf Ferber\, Massachusetts Institute of Technology\nJacob Fox\, Stanford Unviersity\nDavid Gamarnik\, Massachusetts Institute of Technology\nPenny Haxell\, University of Waterloo\nHao Huang\, Emory University\nJeff Kahn\, Rutgers University\nPeter Keevash\, Oxford University\nMichael Krivelevich\, Tel Aviv University\nDaniela Kühn\, University of Birmingham\nShoham Letzer\, ITS Zürich\nShachar Lovett\, University of California\, San Diego\nEyal Lubetzky\, Courant Institute\nRob Morris\, IMPA\nBhargav Narayanan\, Rutgers University\nDeryk Osthus\, University of Birmingham\nJanos Pach\, NYU\nYuval Peres\, Microsoft Redmond\nAlexey Pokryovskyi\, ETH Zürich\nWojciech Samotij\, Tel Aviv University\nLisa Sauermann\, Stanford University\nMathias Schacht\, University of Hamburg\nAlexander Scott\, University of Oxford\nAsaf Shapira\, Tel Aviv University\nJozef Skokan\, London School of Economics\nJoel Spencer\, New York University\nAngelika Steger\, ETH Zurich\nJacques Verstraete\, University of California\, San Diego\nYufei Zhao\, Massachusetts Institute of Technology\nDavid Zuckerman\, University of Texas at Austin\n\nCo-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event\, including participants\, will be updated soon.
URL:https://cmsa.fas.harvard.edu/event/workshop-on-probabilistic-and-extremal-combinatorics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20171113T090000
DTEND;TZID=America/New_York:20171117T160000
DTSTAMP:20260506T034556
CREATED:20230717T173740Z
LAST-MODIFIED:20250304T211529Z
UID:10000040-1510563600-1510934400@cmsa.fas.harvard.edu
SUMMARY:Workshop on Algebraic Methods in Combinatorics
DESCRIPTION:The workshop on Algebraic Methods in Combinatorics will take place November 13-17\, 2017 at the Center of Mathematical Sciences and Applications\, located at 20 Garden Street\, Cambridge\, MA. \nThe main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem\, the distinct distance problem of Erdos and\, more recently\, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra. \nConfirmed participants include: \n\nAbdul Basit\, Rutgers\nBoris Bukh\, Carnegie Mellon University\nPete L. Clark\, University of Georgia\nDavid Conlon\, University of Oxford\nFrank de Zeeuw\, EPFL\nThao Thi Thu Do\, MIT\nNoam Elkies\, Harvard University\nJordan Ellenberg\, University of Wisconsin\nDion Gijswijt\, Delft Institute of Technology\nSivankanth Gopi\, Princeton University\nVenkatesan Guruswami\, Carnegie Mellon University\nMarina Iliopoulou\, University of California\, Berkeley\nRobert Kleinberg\, Cornell University\nMichael Krivelevich\, Tel Aviv University\nVsevelod Lev\, University of Haifa at Oranim\nLászló Miklós Lovász\, UCLA\nBen Lund\, Rutgers\nPéter Pach\, Budapest University of Technology and Economics\nJános Pach\, New York University\nZuzana Patáková\, Institute of Science and Technology Austria\nOrit Raz\, Institute for Advanced Study\nOliver Roche-Newton\, Johannes Kepler University\nMisha Rudnev\, University of Bristol\nAdam Sheffer\, California Institute of Technology\nAmir Shpilka\, Tel-Aviv University\nNoam Solomon\, Harvard CMSA\nJozsef Solymosi\, University of British Columbia\nBenny Sudakov\, ETH\, Zurich\nAndrew Suk\, University of California\, San Diego\nTibor Szabó\, Freie Universität Berlin\nChris Umans\, California Institute of Technology\nAvi Wigderson\, Princeton University\nJosh Zahl\, University of British Columbia\n\nCo-organizers of this workshop include Zeev Dvir\, Larry Guth\, and Shubhangi Saraf. \nMonday\, Nov. 13 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:30am \nVideo\nJozsef Solymosi \n \n\nOn the unit distance problem \nAbstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear\, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}).  \n\n\n\n10:30-11:00am\nCoffee Break\n\n\n\n11:00-12:00pm \nVideo \n \nOrit Raz\nIntersection of linear subspaces in R^d and instances of the PIT problem  \nAbstract: In the talk I will tell about a new deterministic\, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem\, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:30pm \nVideo\nAndrew Hoon Suk\n\nRamsey numbers: combinatorial and geometric \nAbstract:  In this talk\, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon\, Jacob Fox\, Dhruv Mubayi\, Janos Pach\, and Benny Sudakov. \n\n\n\n2:30-3:00pm\nCoffee Break\n\n\n\n3:00-4:00pm \nVideo\nJosh Zahl\n\nCutting curves into segments and incidence geometry \n\n\n\n4:00-6:00pm\nWelcome Reception\n\n\n\n\nTuesday\, Nov. 14 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:30am \nVideo\nPéter Pál Pach\n\nPolynomials\, rank and cap sets \nAbstract: In this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method. \n\n\n\n10:30-11:00am\nCoffee Break\n\n\n\n11:00-12:00pm\nJordan Ellenberg\n\nThe Degeneration Method \nAbstract:  In algebraic geometry\, a very popular way to study (nice\, innocent\, nonsingular) varieties is to degenerate them to (weird-looking\, badly singular\, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method. \n\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:30pm \nVideo\nLarry Guth\nThe polynomial method in Fourier analysis \nAbstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis\, explain the analogy with combinatorial problems\, and discuss how to adapt the polynomial method to the Fourier analysis setting.\n\n\n  \n2:30-3:00pm\nCoffee Break\n\n\n\n3:00-4:00pm\nOpen Problem\n\n\n\n\nWednesday\, Nov. 15 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:30am \n \nAvi Wigderson\n\nThe “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds \nAbstract: Why is it so hard to find a hard function? No one has a clue! In despair\, we turn to excuses called barriers. A barrier is a collection of lower bound techniques\, encompassing as much as possible from those in use\, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic\, and always very far from what we expect for complexity of random functions). \nIn the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem)\,  there are several famous barriers which provide satisfactory excuses\, and point to directions in which techniques may be strengthened. \nIn the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers\, despite some recent interesting  attempts. \nThis talk will describe a new barrier for the Rank Method in arithmetic complexity\, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening). \nI will describe the rank method\, explain how it is used to prove lower bounds\, and then explain its limits via the new barrier result. As an example\, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n\, no rank method can prove a lower bound which exceeds 8n \n(despite the fact that a random such tensor has rank quadratic in n). \nNo special background knowledge is assumed. The audience is expected to come up with new lower bounds\, or else\, with new excuses for their absence. \n\n\n\n10:30-11:00am\nCoffee Break\n\n\n\n11:00-12:00pm \nVideo\nVenkat Guruswami\n\nSubspace evasion\, list decoding\, and dimension expanders \n Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields\, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*. \nSubspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular\, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field\, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast\, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further\, in recent (ongoing) work\, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree. \nThis talk will survey these developments revolving around subspace designs\, their motivation\, construction\, analysis\, and connections. \n(Based on several joint works whose co-authors include Chaoping Xing\, Swastik Kopparty\, Michael Forbes\, Nicolas Resch\, and Chen Yuan.) \n\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:30pm \n \nDavid Conlon\n\nFinite reflection groups and graph norms \nAbstract: For any given graph $H$\, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction\, Hatami showed that even cycles\, complete bipartite graphs\, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups\, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular\, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee. \n \n\n\n2:30-3:00pm\nCoffee Break\n\n\n\n3:00-4:00pm \nVideo\nLaszlo Miklós Lovasz\n\nRemoval lemmas for triangles and k-cycles. \nAbstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n\, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k\, epsilon>0 and prime p\, there is a delta>0 such that if we have a collection of k sets in F_p^n\, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n\, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma\, and\, in particular\, asked whether a polynomial bound holds. Despite considerable attention\, prior to our work\, the best known bound for any k\, due to Fox\, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k). \nIn this talk\, we will discuss recent work on Green’s problem. For triangles\, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n\, using the recent breakthroughs with the polynomial method. For k-cycles\, we also prove a polynomial bound\, however\, the question of the optimal exponent is still open. \nThe triangle case is joint work with Jacob Fox\, and the k-cycle case with Jacob Fox and Lisa Sauermann. \n\n\n\n\nThursday\, Nov. 16 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:30am \nVideo\nJanos Pach\nLet’s talk about multiple crossings \nAbstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other\, they have a nonempty intersection\, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers\, including a recent result of Kupavskii\, Tomon\, and the speaker\, improving a 40 years old bound of Lomonosov.\n\n\n10:30-11:00am\nCoffee Break\n\n\n\n11:00-12:00pm \nVideo\nMisha Rudnev\n\nFew products\, many sums \nAbstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”\, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress\, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality \n$$ \n|A|^{10} \ll |A-A|^4|AA|^4 \n$$ \nto \n$$|A|^{10}\lesssim |A-A|^3|AA|^5.$$ \nThe other is the bound  \n$$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$. \n\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:30pm \nVideo\nAdam Sheffer\n\nGeometric Energies: Between Discrete Geometry and Additive Combinatorics \nAbstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies\, and uses those to derive new bounds for several problems in Discrete Geometry.   \n\n\n\n2:30-3:00pm\nCoffee Break\n\n\n\n3:00-4:00pm \nVideo\nBoris Bukh\n\nRanks of matrices with few distinct entries \nAbstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk\, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists. \n\n\n\n\nFriday\, Nov. 17 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:30am \nVideo\nBenny Sudakov\n\nSubmodular minimization and set-systems with restricted intersections \nAbstract: Submodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly\, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints\, i.e.\, optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem\, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value. \nWe show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints\, i.e.\, over all sets (of any given lattice) of cardinality r mod m\, as long as m is a constant prime power. To obtain our results\, we combine tools from Combinatorial Optimization\, Combinatorics\, and Number Theory. In particular\, we establish an interesting connection between the correctness of a natural algorithm\, and the non-existence of set systems with specific intersection properties. \nJoint work with M. Nagele and R. Zenklusen \n\n\n\n10:30-11:00am\nCoffee Break\n\n\n\n11:00-12:00pm \nVideo\nRobert Kleinberg\n  \nExplicit sum-of-squares lower bounds via the polynomial method \nAbstract: The sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities\, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials\, and while any unsatisfiable system of inequalities has a sum-of-squares refutation\, the sos polynomials involved might have arbitrarily high degree. However\, if a system admits a refutation where all polynomials involved have degree at most d\, then the refutation can be found by an algorithm with running time polynomial in N^d\, where N is the combined number of variables and inequalities in the system. \nLow-degree sum-of-squares refutations appear throughout mathematics. For example\, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory\, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control. \nTherefore\, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently\, the only known examples were either not explicit (i.e.\, known to exist by non-constructive means such as the probabilistic method) or not robust (i.e.\, a system is constructed which is not refutable by degree d sos polynomials\, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem\, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust. \nThis is joint work with Sam Hopkins. \n\n\n\n12:00-1:30pm\nLunch\n\n\n\n\n  \n\n\n\nEvents\,Past Events\,Programs
URL:https://cmsa.fas.harvard.edu/event/workshop-on-algebraic-methods-in-combinatorics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20171002T090000
DTEND;TZID=America/New_York:20171006T160000
DTSTAMP:20260506T034556
CREATED:20230717T173144Z
LAST-MODIFIED:20250304T211134Z
UID:10000037-1506934800-1507305600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Additive Combinatorics\, Oct. 2-6\, 2017
DESCRIPTION:The workshop on additive combinatorics will take place October 2-6\, 2017 at the Center of Mathematical Sciences and Applications\, located at 20 Garden Street\, Cambridge\, MA. \nAdditive combinatorics is a mathematical area bordering on number theory\, discrete mathematics\, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions\, such as: \n\nThe first sensible bounds for Szemerédi’s theorem on progressions (Gowers);\nLinear patterns in the primes (Green\, Tao\, Ziegler);\nConstruction of expanding sets in groups and expander graphs (Bourgain\, Gamburd);\nThe Kakeya Problem in Euclidean harmonic analysis (Bourgain\, Katz\, Tao).\n\nIdeas and techniques from additive combinatorics have also had an impact in theoretical computer science\, for example \n\nConstructions of pseudorandom objects (eg. extractors and expanders);\nConstructions of extremal objects (eg. BCH codes);\nProperty testing (eg. testing linearity);\nAlgebraic algorithms (eg. matrix multiplication).\n\nThe main focus of this workshop will be to bring together researchers involved in additive combinatorics\, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n \, which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics\, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture\, inverse theorems for the Gowers norms with bounds\, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt. \nConfirmed participants include: \n\nArnab Bhattacharyya (Indian Institute of Science)\nThomas Bloom (University of Bristol)\nJop Briët (Centrum Wiskunde & Informatica\, Amsterdam)\nMei-Chu Chang (University of California\, Riverside)\nNoam Elkies (Harvard University)\nAsaf Ferber (MIT)\nJacob Fox (Stanford University)\nShafi Goldwasser (MIT)\nElena Grigorescu (Purdue University)\nHamed Hatami (McGill University)\nPooya Hatami (Institute for Advanced Study)\nKaave Hosseini (University of California\, San Diego)\nGuy Kindler (Hebrew University of Jerusalem)\nVsevolod Lev (University of Haifa at Oranim)\nSean Prendiville (University of Manchester)\nRonitt Rubinfeld (MIT)\nWill Sawin (ETH Zürich)\nFernando Shao (Oxford University)\nOlof Sisask (KTH Royal Institute of Technology)\nMadhur Tulsiani (University of Chicago)\nJulia Wolf (University of Bristol)\nEmanuele Viola (Northeastern University)\nYufei Zhao (MIT)\n\nCo-organizers of this workshop include Ben Green\, Swastik Kopparty\, Ryan O’Donnell\, Tamar Ziegler. \nMonday\, October 2 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n \n\n\n9:30-10:20am\nJacob Fox\nTower-type bounds for Roth’s theorem with popular differences \nAbstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$\, any subset of $\{1\, \dots\, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression\, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is\, for every $\epsilon > 0$\, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1\, \dots\, n\}$ with density $\alpha$\, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary. \nThe first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.\n\n\n10:20-11:00am\nCoffee Break\n \n\n\n11:00-11:50am\nYufei Zhao\nTower-type bounds for Roth’s theorem with popular differences \nAbstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.\n\n\n12:00-1:30pm\nLunch\n \n\n\n1:30-2:20pm\nJop Briët\nLocally decodable codes and arithmetic progressions in random settings \nAbstract: This talk is about a common feature of special types of error correcting codes\, so-called locally decodable codes (LDCs)\, and two problems on arithmetic progressions in random settings\, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices\, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings. \nJoint work with Sivakanth Gopi\n\n\n2:20-3:00pm\nCoffee Break\n \n\n\n3:00-3:50pm\nFernando Shao\n\nLarge deviations for arithmetic progressions \nAbstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work\, namely concerning the “complexity” of the dual functions of AP-counts. \n\n\n\n4:00-6:00pm\nWelcome Reception\n\n\n\n\nTuesday\, October 3 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:20am\nEmanuele Viola\nInterleaved group products \nAuthors: Timothy Gowers and Emanuele Viola \nAbstract: Let G be the special linear group SL(2\,q). We show that if (a1\,a2) and (b1\,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example\, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2\, then a pointwise product of s independent copies of X is nearly uniform in G^m\, where s depends on m only. Similar statements can be made for other groups as well. \nThese results have applications in computer science\, which is the area where they were first sought by Miles and Viola (2013).\n\n\n10:20-11:00am\nCoffee Break\n\n\n\n11:00-11:50am\nVsevolod Lev\nOn Isoperimetric Stability \nAbstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular\, if $A$ and $S$ are finite\, non-empty subsets of an abelian group such that $S$ is independent\, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0\,1]$\, then $|A|\ge4^{(1-1/d)c|S|}$\, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible. \nAs a corollary\, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$\, our bound translates into a sharp estimate for the additive  dimension of the popular difference set. \nWe also prove\, as an auxiliary result\, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite\, non-empty downset\, then\, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$\, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\\, \log_2 |A|. $$\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:20pm\nElena Grigorescu\nNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem \nAbstract: I will discuss the complexity of decoding Reed-Solomon codes\, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments\, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory\, which turns out to capture a main barrier in extending our techniques to smaller radii. \nJoint work with Venkata Gandikota and Badih Ghazi.\n\n\n2:20-3:00pm\nCoffee Break\n\n\n\n3:00-3:50pm\nSean Prendiville\nPartition regularity of certain non-linear Diophantine equations. \nAbstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest\, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.\n\n\n\nWednesday\, October 4 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n \n\n\n9:30-10:20am\nOlof Sisask\nBounds on capsets via properties of spectra \nAbstract: A capset in F_3^n is a subset A containing no three distinct elements x\, y\, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics\, particularly motivated by the corresponding question for subsets of {1\,2\,…\,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt\, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting\, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis\, and in particular the properties of large spectra. This will be a two part talk\, in which many of the ideas will be outlined in the first talk\, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk\, by Thomas Bloom\, together with ideas on how one might hope to achieve Behrend-style bounds using this method. \nJoint work with Thomas Bloom.\n\n\n10:20-11:00am\nCoffee Break\n \n\n\n11:00-11:50am\nThomas Bloom\nBounds on capsets via properties of spectra \nThis is a continuation of the previous talk by Olof Sisask.\n\n\n12:00-1:30pm\nLunch\n \n\n\n1:30-2:20pm\nHamed Hatami\nPolynomial method and graph bootstrap percolation \nAbstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel\, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.\n\n\n2:20-3:00pm\nCoffee Break\n\n\n\n3:00-3:50pm\nArnab Bhattacharyya\nAlgorithmic Polynomial Decomposition \nAbstract: Fix a prime p. Given a positive integer k\, a vector of positive integers D = (D_1\, …\, D_k) and a function G: F_p^k → F_p\, we say a function P: F_p^n → F_p admits a (k\, D\, G)-decomposition if there exist polynomials P_1\, …\, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n\, P(x) = G(P_1(x)\, …\, P_k(x)). For instance\, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2\, (d-1\, d-1)\, prod)-decomposition where prod(a\,b) = ab. \nWhen show that for any fixed k\, D\, G\, and fixed bound d\, we can decide whether a given polynomial P(x_1\, …\, x_n) of degree d admits a (k\,D\,G)-decomposition and if so\, find a witnessing decomposition\, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions. \nJoint work with Pooya Hatami\, Chetan Gupta and Madhur Tulsiani.\n\n\n\nThursday\, October 5 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:20am\nMadhur Tulsiani\nHigher-order Fourier analysis and approximate decoding of Reed-Muller codes \n Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions. \nI will discuss constructive proofs of these decompositions based on boosting\, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem. \nBased on joint works with Arnab Bhattacharyya\, Eli Ben-Sasson\, Pooya Hatami\, Noga Ron-Zewi and Julia Wolf.\n\n\n10:20-11:00am\nCoffee Break\n\n\n\n11:00-11:50am\nJulia Wolf\nStable arithmetic regularity \nThe arithmetic regularity lemma in the finite-field model\, proved by Green in 2005\, states that given a subset A of a finite-dimensional vector space over a prime field\, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general\, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity\, and that one must allow for a small number of non-uniform cosets. \nOur main result is that\, under a natural model-theoretic assumption of stability\, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically\, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity\, and in which there are no non-uniform cosets. \nThis is joint work with Caroline Terry. \n\n\n\n12:00-1:30pm\nLunch\n \n\n\n1:30-2:20pm\nWill Sawin\n\nConstructions of Additive Matchings \nAbstract: I will explain my work\, with Robert Kleinberg and David Speyer\, constructing large tri-colored sum-free sets in vector spaces over finite fields\, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers.  \n\n\n\n2:20-3:00pm\nCoffee Break\n\n\n\n3:00-3:50pm\nMei-Chu Chang\nArithmetic progressions in multiplicative groups of finite fields \nAbstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough\, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.\n\n\n\nFriday\, October 6 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n9:00-9:30am\nBreakfast\n\n\n\n9:30-10:20am\nAsaf Ferber\nOn a resilience version of the Littlewood-Offord problem \nAbstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is\, consider the sum X=a_1x_1+…a_nx_n\, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices\, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems. \nJoint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH\, Zurich).\n\n\n10:20-11:00am\nCoffee Break\n\n\n\n11:00-11:50am\nKaave Hosseini\nProtocols for XOR functions and Entropy decrement \nAbstract: Let f:F_2^n –> {0\,1} be a function and suppose the matrix M defined by M(x\,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words\, up to polynomial factors\, deterministic communication complexity and parity decision tree complexity are equivalent. \nThis relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma. \nJoint work with Hamed Hatami and Shachar Lovett\n\n\n12:00-1:30pm\nLunch\n\n\n\n1:30-2:20pm\nGuy Kindler\n\nFrom the Grassmann graph to Two-to-Two games \nAbstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically\, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al.\, one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture. \nThe latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02]\, which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed\, if the Grassmann-Graph conjecture its true\, it would also rule out some attempts to refute the Unique-Games conjecture\, as these attempts provide potentially efficient algorithms to solve unique games\, that would actually also solve two-to-two games if they work at all. \nThese new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure. \nThis is joint work with Irit Dinur\, Subhash Khot\, Dror Minzer\, and Muli Safra. \n\n\n\n\n\n\n\nEvents\,Past Events
URL:https://cmsa.fas.harvard.edu/event/workshop-on-additive-combinatorics-oct-2-6-2017/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170418T110000
DTEND;TZID=America/New_York:20170418T120000
DTSTAMP:20260506T034556
CREATED:20240213T093734Z
LAST-MODIFIED:20240220T144719Z
UID:10002348-1492513200-1492516800@cmsa.fas.harvard.edu
SUMMARY:4-18-2017 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-18-2017-social-science-applications-forum/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170324T100000
DTEND;TZID=America/New_York:20170324T110000
DTSTAMP:20260506T034556
CREATED:20240213T102725Z
LAST-MODIFIED:20240220T143442Z
UID:10002428-1490349600-1490353200@cmsa.fas.harvard.edu
SUMMARY:3-24-2017 Random Matrix & Probability Theory Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-24-2017-random-matrix-probability-theory-seminar/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170308T121100
DTEND;TZID=America/New_York:20170419T121100
DTSTAMP:20260506T034556
CREATED:20230717T174006Z
LAST-MODIFIED:20250328T194543Z
UID:10000024-1488975060-1492603860@cmsa.fas.harvard.edu
SUMMARY:Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
DESCRIPTION:From March 8 to April 19\, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am\, which will be recorded and promptly available on CMSA’s Youtube Channel.
URL:https://cmsa.fas.harvard.edu/event/special-lecture-series-on-donaldson-thomas-and-gromov-witten-theories/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20161203T090000
DTEND;TZID=America/New_York:20161204T170000
DTSTAMP:20260506T034556
CREATED:20230717T172404Z
LAST-MODIFIED:20250305T201523Z
UID:10000018-1480755600-1480870800@cmsa.fas.harvard.edu
SUMMARY:Mini-school on Nonlinear Equations\, December 3-4\, 2016
DESCRIPTION: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. \nSpeakers:\n\nCliff Taubes (Harvard University)\nValentino Tosatti (Northwestern University)\nPengfei Guan (McGill University)\nJared Speck (MIT)\n\nSchedule:\n\n\n\nDecember 3rd – Day 1\n\n\n9:00am – 10:30am\nCliff Taubes\, “Compactness theorems in gauge theories”\n\n\n10:45am – 12:15pm\nValentino Tosatti\, “Complex Monge-Ampère Equations”\n\n\n\n\n\n12:15pm – 1:45pm\nLUNCH\n\n\n\n\n\n\n1:45pm – 3:15pm\nPengfei Guan\, “Monge-Ampère type equations and related geometric problems”\n\n\n3:30pm – 5:00pm\nJared Speck\, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”\n\n\n\n\n\n\n\n\nDecember 4th – Day 2\n\n\n9:00am – 10:30am\nCliff Taubes\, “Compactness theorems in gauge theories”\n\n\n10:45am – 12:15pm\nValentino Tosatti\, “Complex Monge-Ampère Equations”\n\n\n\n\n\n12:15pm – 1:45pm\nLUNCH\n\n\n\n\n\n\n1:45pm – 3:15pm\nPengfei Guan\, “Monge-Ampère type equations and related geometric problems”\n\n\n3:30pm – 5:00pm\nJared Speck\, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”\n\n\n\n\n  \n* This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.
URL:https://cmsa.fas.harvard.edu/event/mini-school-on-nonlinear-equations-december-3-4-2016/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/minischool.png
END:VEVENT
END:VCALENDAR