Entanglement Entropy in Flat Holography

Wei Song
Member, School of Natural Sciences, Institute for Advanced Study; Tsinghua University
May 15, 2020
The appearance of BMS symmetry as the asymptotic symmetry of Minkowski spacetime suggests a holographic relation between Einstein gravity and quantum field theory with BMS invariance, dubbed BMSFT. With a three dimensional bulk, the dual BMSFT is a non-Lorentz invariant, two dimensional field theory with infinite-dimensional symmetries. In this talk, I will argue that entanglement entropy in BMSFT can be described by a swing surface in the bulk.

MathZero, The Classification Problem, and Set-Theoretic Type Theory

David McAllester
Toyota Technological Institute at Chicago
May 14, 2020
AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics --- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem --- the problem of classifying concept instances up to isomorphism. Isomorphism is central to the structure of mathematics.

Convex Set Disjointness, Distributed Learning of Halfspaces, and Linear Programming

Shay Moran
Member, School of Mathematics
May 12, 2020
Distributed learning protocols are designed to train on distributed data without gathering it all on a single centralized machine, thus contributing to the efficiency of the system and enhancing its privacy. We study a central problem in distributed learning, called Distributed Learning of Halfspaces: let U \subset R^d be a known domain of size n and let h:R^d —> R be an unknown target affine function. A set of examples {(u,b)} is distributed between several parties, where u \in U is a point and b = sign(h(u)) \in {-1, +1} is its label.

Quantitative decompositions of Lipschitz mappings

Guy C. David
Ball State University
May 12, 2020
Given a Lipschitz map, it is often useful to chop the domain into pieces on which the map has simple behavior. For example, depending on the dimensions of source and target, one may ask for pieces on which the map behaves like a bi-Lipschitz embedding or like a linear projection. For many issues, it is even more useful if this decomposition is quantitative, i.e., with bounds independent of the particular map or spaces involved.

Generative Modeling by Estimating Gradients of the Data Distribution

Stefano Ermon
Stanford University
May 12, 2020
Existing generative models are typically based on explicit representations of probability distributions (e.g., autoregressive or VAEs) or implicit sampling procedures (e.g., GANs). We propose an alternative approach based on modeling directly the vector field of gradients of the data distribution (scores). Our framework allows flexible energy-based model architectures, requires no sampling during training or the use of adversarial training methods.

Using discrepancy theory to improve the design of randomized controlled trials

Daniel Spielman
Yale University
May 11, 2020
In randomized experiments, such as a medical trials, we randomly assign the treatment, such as a drug or a placebo, that each experimental subject receives. Randomization can help us accurately estimate the difference in treatment effects with high probability. We also know that we want the two groups to be similar: ideally the two groups would be similar in every statistic we can measure beforehand. Recent advances in algorithmic discrepancy theory allow us to divide subjects into groups with similar statistics.

Spectral characterizations of Besse and Zoll Reeb flows

Marco Mazzucchelli
École normale supérieure de Lyon
May 8, 2020
In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian geometry, Reeb flows all of whose orbits are closed are sometimes called Besse, and Besse Reeb flows all of whose orbits have the same minimal period are sometimes called Zoll.

On Math, Shadows, and Digital Sundials

Silvia Ghinassi
School of Mathematics
May 8, 2020
Geometric measure theory is a branch of mathematics that, loosely said, focuses on studying geometric properties of objects, such as size and shape. In this talk, Silvia Ghinassi will discuss: How do we measure size? How do we know when an object is one-dimensional, or two-dimensional? What if it is neither? How can we describe shape? What does a cylinder look like if I look at it from below? And from the side?

Learning probability distributions; What can, What can't be done

Shai Ben-David
University of Waterloo
May 7, 2020
A possible high level description of statistical learning is that it aims to learn about some unknown probability distribution ("environment”) from samples it generates ("training data”). In its most general form, assuming no prior knowledge and asking to find accurate approximations to the data generating distributions, there can be no success guarantee. In this talk I will discuss two major directions of relaxing that too hard problem.