9/10/2020 Quantum Matter Seminar
2020-09-10 10:30 - 12:00 (America/New_York) | MA

Existence of Canonical Metrics on Non-Kähler Geometry
2020-09-10 14:23 - 14:24 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on Existence of Canonical Metrics on Non-Kähler Geometry.
In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia University.
More information about this talk can be found on the Simons Foundation website.

9/14/2020 Mathematical Physics Seminar
2020-09-14 10:30 - 11:30 | MA

9/15/2020 Computer Science for Mathematicians
2020-09-15 11:30 - 12:30 | Virtual

9/16/2020 Quantum Matter Seminar
2020-09-16 10:30 - 12:00 | MA

Graph Representation Learning: Recent Advances and Open Challenges
2020-09-16 15:00 - 16:00 | Virtual
Speaker: William Hamilton, McGill University and MILA
Title: Graph Representation Learning: Recent Advances and Open Challenges
Abstract: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial if we want systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, most prominently in the development of graph neural networks (GNNs). Advances in GNNs have led to state-of-the-art results in numerous domains, including chemical synthesis, 3D-vision, recommender systems, question answering, and social network analysis. In the first part of this talk I will provide an overview and summary of recent progress in this fast-growing area, highlighting foundational methods and theoretical motivations. In the second part of this talk I will discuss fundamental limitations of the current GNN paradigm and propose open challenges for the theoretical advancement of the field.

9/17/20 Quantum Matter Seminar
2020-09-17 10:30 - 12:00 | MA

9/21/2020 Math-Physics Seminar
2020-09-21 10:30 - 11:30 | MA

9/22/2020 Computer Science for Mathematicians
2020-09-22 11:30 - 12:30 | MA

CMSA Math-Science Literature Lecture: Hodge structures and the topology of algebraic varieties
2020-09-23 09:00 - 2020-09-30 09:06 | Virtual
Claire Voisin (Collège de France)
Title: Hodge structures and the topology of algebraic varieties
Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results we will discuss rely on Hodge theory, which has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization, is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives.
Talk chair: Joe Harris
Video | Slides | Article

9/23/2020 Strongly Correlated Quantum Materials Series
2020-09-23 10:30 - 12:00 | MA

Self-induced regularization from linear regression to neural networks
2020-09-23 15:00 - 16:00 | Virtual
Speaker: Andrea Montanari, Departments of Electrical Engineering and Statistics, Stanford
Title: Self-induced regularization from linear regression to neural networks
Abstract: Modern machine learning methods –most noticeably multi-layer neural networks– require to fit highly non-linear models comprising tens of thousands to millions of parameters. Despite this, little attention is paid to the regularization mechanism to control model’s complexity. Indeed, the resulting models are often so complex as to achieve vanishing training error: they interpolate the data. Despite this, these models generalize well to unseen data : they have small test error. I will discuss several examples of this phenomenon, beginning with a simple linear regression model, and ending with two-layers neural networks in the so-called lazy regime. For these examples precise asymptotics could be determined mathematically, using tools from random matrix theory. I will try to extract a unifying picture. A common feature is the fact that a complex unregularized nonlinear model becomes essentially equivalent to a simpler model, which is however regularized in a non-trivial way. [Based on joint papers with: Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, Feng Ruan, Youngtak Sohn, Jun Yan, Yiqiao Zhong]

9/24/2020 Strongly Correlated Quantum Materials
2020-09-24 12:00 - 13:30 | MA

CMSA Math-Science Literature Lecture: Area-minimizing integral currents and their regularity
2020-09-25 09:00 - 10:30 | Virtual
Camillo De Lellis (IAS)
Title: Area-minimizing integral currents and their regularity
Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding.
Talk Chair: William Minicozzi
Video

CMSA Math-Science Literature Lecture: From Deep Learning to Deep Understanding
2020-09-28 09:00 - 12:13 | Virtual
Harry Shum (Tsinghua University)
Title: From Deep Learning to Deep Understanding
Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model, and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.
Talk chair: Shing-Tung Yau
Video

9/28/2020 Mathematical Physics Seminar
2020-09-28 11:00 - 12:00 | MA

CMSA Math-Science Literature Lecture: A personal story of the 4D Poincare conjecture
2020-09-28 12:30 - 14:00 | Virtual
Michael Freedman (Microsoft – Station Q)
Title: A personal story of the 4D Poincare conjecture
Abstract: The proof of PC4 involved the convergence of several historical streams. To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.
Talk Chair: Peter Kronheimer
Video

9/29/2020 Computer Science for Mathematicians
2020-09-29 11:30 - 12:30 | MA

9/30/2020 Quantum Matter Seminar
2020-09-30 10:30 - 12:00 | MA

CMSA Math-Science Literature Lecture: Immersions of manifolds and homotopy theory
2020-09-30 12:00 - 13:30 | Virtual
Ralph Cohen (Stanford University)
Title: Immersions of manifolds and homotopy theory
Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.
Talk chair: Michael Hopkins
Video

10/1/2020 Quantum Matter seminar
2020-10-01 10:30 - 12:00 | MA

CMSA Math-Science Literature Lecture: Birational geometry
2020-10-02 10:45 - 12:15 | Virtual
Vyacheslav V. Shokurov (Johns Hopkins University)
Title: Birational geometry
Abstract: About main achievements in birational geometry during the last fifty years.
Talk chair: Caucher Birkar
Video

CMSA Math-Science Literature Lecture: Kunihiko Kodaira and complex manifolds
2020-10-05 08:00 - 09:30 | Virtual
Yujiro Kawamata (University of Tokyo)
Title: Kunihiko Kodaira and complex manifolds
Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions. After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces. Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.
Talk chair: Baohua Fu
Video

10/05/2020 Math Physics Seminar
2020-10-05 10:30 - 12:00 | MA

4/15/2020 Quantum Matter seminar
2020-10-05 10:30 - 12:00 | MA

10/6/2020 Computer Science for Mathematicians
2020-10-06 11:30 - 12:30 | MA

10/7/2020 Quantum Matter Seminar
2020-10-07 10:30 - 12:00 | MA

10/8/2020 Quantum Matter Seminar
2020-10-08 10:30 - 12:00 | MA

Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers
2020-10-14 09:00 - 10:00 | MA
Speaker: Gil Kalai (Hebrew University and IDC Herzliya)
Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers
Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to

a) My general argument “against” quantum computers,
b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
Relevant papers:
Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.wordpress.com/2019/11/stat-quantum2.pdf
Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.wordpress.com/2020/08/laws-blog2.pdf
Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.wordpress.com/2019/09/main-pr.pdf

10/14/2020 Quantum Matter Seminar
2020-10-14 10:30 - 12:00 | MA
