CMSA

4/6/2021 Computer Science for Mathematicians
2021-04-06 11:30 - 12:30 (America/New_York) | MA

4/7/2021 Quantum Matter in Mathematics and Physics
2021-04-07 10:30 - 12:00 | MA

4/7/2021 Random Matrix and Probability Theory Seminar
2021-04-07 14:00 - 15:00 | MA

Type theory from the perspective of artificial intelligence
2021-04-07 15:00 - 16:00 | MA
Speaker: David McAllester – Toyota Technological Institute at Chicago
Title: Type theory from the perspective of artificial intelligence
Abstract: This talk will discuss dependent type theory from the perspective of artificial intelligence and cognitive science. From an artificial intelligence perspective it will be argued that type theory is central to defining the “game” of mathematics — an action space and reward structure for pure mathematics. From a cognitive science perspective type theory provides a model of the grammar of the colloquial (natural) language of mathematics. Of particular interest is the notion of a signature-axiom structure class and the three fundamental notions of equality in mathematics — set-theoretic equality between structure elements, isomorphism between structures, and Birkoff and Rota’s notion of cryptomorphism between structure classes. This talk will present a version of type theory based on set-theoretic semantics and the 1930’s notion of structure and isomorphism given by the Bourbaki group of mathematicians. It will be argued that this “Bourbaki type theory” (BTT) is more natural and accessible to classically trained mathematicians than Martin-Löf type theory (MLTT). BTT avoids the Curry-Howard isomorphism and axiom J of MLTT. The talk will also discuss BTT as a model of MLTT. The BTT model is similar to the groupoid model in that propositional equality is interpreted as isomorphism but different in various details. The talk will also briefly mention initial thoughts in defining an action space and reward structure for a game of mathematics.

CMSA Math-Science Literature Lecture: Quantum error correcting codes and fault tolerance
2021-04-08 09:00 - 10:30 | Virtual
Peter Shor (MIT)
Title: Quantum error correcting codes and fault tolerance
Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.

Talk chair: Zhengwei Liu
Video

4/8/2021 Interdisciplinary Science Seminar
2021-04-08 12:00 - 13:00 | MA

4/8/2021 Quantum Matter Seminar
2021-04-08 13:00 - 14:30 | MA

4/12/2021 Mathematical Physics Seminar
2021-04-12 10:00 - 11:00 | MA

4/14/2021 Quantum Matter Seminar
2021-04-14 10:30 - 12:00 | 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.
