4/14/2021 Quantum Matter Seminar
2021-04-14 10:30 - 12:00 (America/New_York) | MA

A Bayesian neural network predicts the dissolution of compact planetary systems
2021-04-14 15:00 - 16:00 | Virtual
Speaker: Miles Cranmer – Princeton University
Title: A Bayesian neural network predicts the dissolution of compact planetary systems
Abstract: Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. I will discuss our deep learning architecture (arxiv:2101.04117) which pushes forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics, our new technique learns its own metrics from scratch, enabled by a novel internal structure inspired from dynamics theory. The Bayesian neural network model can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short N-body time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on three-planet configurations, the model demonstrates robust generalization to five-planet systems, even outperforming models designed for that specific set of integrations. I will also discuss some work on recovering symbolic representations of such models using arxiv:2006.11287.

4/15/2021 Interdisciplinary Science Seminar
2021-04-15 09:00 - 10:00 | Virtual

4/15/2021 Quantum Matter in Mathematics Seminar
2021-04-15 10:30 - 12:00 | MA

4/20/2021 Computer Science for Mathematicians
2021-04-15 11:30 - 12:30 | MA

CMSA Math-Science Literature Lecture: Deep Networks from First Principles
2021-04-16 13:00 - 14:30 | Virtual
Yi MaPhoto Copyright Noah Berger / 2019

Yi Ma (University of California, Berkeley)
Title: Deep Networks from First Principles
Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.
Talk chair: Harry Shum
Slides | Video

4/16/2021 Random Matrix and Probability Theory Seminar
2021-04-16 14:00 - 15:00 | Virtual

4/19/2021 Mathematical Physics Seminar
2021-04-19 10:00 - 11:00 | Virtual

CMSA Math-Science Literature Lecture: The Atiyah-Singer Index Theorem
2021-04-20 09:00 - 10:30 | Virtual
Dan Freed (The University of Texas at Austin)
Title: The Atiyah-Singer Index Theorem
Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator.
This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.
Talk chair: Cumrun Vafa
Video

4/21/2021 Quantum Matter Seminar
2021-04-21 10:30 - 12:00 | Virtual

4/21/2021 Random Matrix and Probability Theory Seminar
2021-04-21 14:00 - 15:00 | MA

Homotopy type theory and the quest for extensionality
2021-04-21 15:00 - 16:00 | Virtual
Speaker: Michael Shulman – Dept. of Mathematics, University of San Diego
Title: Homotopy type theory and the quest for extensionality
Abstract: Over the past decades, dependent type theory has proven to be a powerful framework for verified software and formalized mathematics. However, its treatment of equality has always been somewhat uncomfortable. Recently, homotopy type theory has made progress towards a more useful notion of equality, which natively implements both isomorphism-invariance in mathematics and representation-independence in programming. This progress is based on ideas from abstract homotopy theory and higher category theory, and with the development of cubical type theories it can be implemented as a true programming language. In this talk, I will survey these developments and their potential applications, and suggest some directions for further improvement.

4/22/2021 Interdisciplinary Science Seminar
2021-04-22 09:00 - 10:00 | MA

4/22/2021 Quantum Matter Seminar
2021-04-22 10:30 - 12:00 | Virtual

CMSA Math-Science Literature Lecture: Indistinguishability Obfuscation: How to Hide Secrets within Software
2021-04-23 16:00 - 18:30 | Virtual
Amit Sahai (UCLA)
Title: Indistinguishability Obfuscation: How to Hide Secrets within Software
Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades.
In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming, introduced in our work with Waters in 2013, well over a hundred papers have explored the remarkable power of iO.
We’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin, finally showing how to construct iO in such a way that, for the first time, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography.
Talk chair: Sergiy Verstyuk
Video

4/26/2021 Math Physics Seminar
2021-04-26 10:00 - 11:00 | Virtual

CMSA Math-Science Literature Lecture: Moment maps and the Yang-Mills functional
2021-04-27 09:00 - 10:30 | Virtual
Frances Kirwan (University of Oxford)
Title: Moment maps and the Yang-Mills functional
Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led.
This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.
Talk chair: Peter Kronheimer
Video

4/28/2021 Quantum Matter Seminar
2021-04-28 13:00 - 14:30 | MA

4/29/2021 Interdisciplinary Science Seminar
2021-04-29 09:00 - 10:00 | MA

4/29/2021 Quantum Matter Seminar
2021-04-29 10:30 - 12:00 | MA

Computational Biology Symposium
2021-05-03 10:00 - 16:00 | 20 Garden Street, Cambridge, MA 02138, MA, MA, 02138, United States
On May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo.
The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch.
Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.
Confirmed participants:

Uri Alon, Weizmann Institute
Elana Fertig, Johns Hopkins
Martin Hemberg, Brigham and Women’s Hospital
Peter Kharchenko, Harvard University
Smita Krishnaswamy, Yale University
John Marioni, EMBL-EBI
Eran Segal, Weizmann Institute
Meromit Singer, Harvard Medical School

Schedule:
PDF of the schedule Download

Rank-Based Independence Testing in Near Linear Time
2021-05-04 10:30 - 12:30 | MA
Speaker: Chaim Even-Zohar (Alan Turing Institute, London)
Title: Rank-Based Independence Testing in Near Linear Time
Abstract: In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.
We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.
Joint work with Calvin Leng.

5/5/2021 Quantum Matter Seminar
2021-05-05 20:00 - 21:30 | MA

5/6/2021 Interdisciplinary Science Seminar
2021-05-06 09:00 - 10:00 | MA

5/6/2021 Quantum Matter Seminar
2021-05-06 10:30 - 12:00 | MA

FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
2021-05-07 11:00 - 2021-05-09 20:45 | Virtual
This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom
The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data.
This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.
The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.
For the discussions, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com.
We invite junior researchers to present a short talk in the workshop. The session will be held on Friday, May 7th or Saturday, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd.

Organizers:

David Glickenstein, University of Arizona
Joel Hass, University of California, Davis
Patrice Koehl, University of California, Davis
Feng Luo, Rutgers University, New Brunswick
Tianqi Wu, Harvard University
Shing-Tung Yau, Harvard University

Featured lectures:

Christopher Bishop, Stony Brook
Keenan Crane, Carnegie Mellon

Speakers include:

Miri Ben-Chen, Technion – Israel Institute of Technology
Alexander Bobenko, Technische Universität Berlin, Germany
Ulrike Buecking, Free University, Germany
Nadav Dym, Duke University
Ivan Izmestiev, Vienna University of Technology
Yanwen Luo, Rutgers
Stephan Tillmann, The University of Sydney
Max Wardetzky, University of Goettingen
Xu Xu, Wuhan University

5/11/2021 Computer Science for Mathematicians
2021-05-11 11:30 - 12:30 | MA

5/12/2021 Strongly Correlated Quantum Materials
2021-05-12 10:30 - 12:00 | MA

5/13/2021 Interdisciplinary Science Seminar
2021-05-13 09:00 - 10:00 | MA

5/13/2021 Quantum Matter Seminar
2021-05-13 10:30 - 12:00 | MA
