On triple product L functions

Jayce Robert Getz
Duke University
May 7, 2020
Establishing the conjectured analytic properties of triple product L-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on GL_3; in some sense this is the smallest case that appears out of reach via standard techniques. The approach is based on the beautiful fibration method of Braverman and Kazhdan for constructing Schwartz spaces and proving analogues of the Poisson summation formula.

Cutting Planes Proofs of Tseitin and Random Formulas

Noah Fleming
University of Toronto
May 5, 2020
Proof Complexity studies the length of proofs of propositional tautologies in various restricted proof systems. One of the most well-studied is the Cutting Planes proof system, which captures reasoning which can be expressed using linear inequalities. A series of papers proved lower bounds on the length of Cutting Planes using the method of feasible interpolation whereby proving lower bounds on the size of Cutting Planes lower bounds proofs of a certain restricted class of formulas is reduced to monotone circuit lower bounds.

Boosting Simple Learners

Shay Moran
Google
May 5, 2020
We study boosting algorithms under the assumption that the given weak learner outputs hypotheses from a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are “rules-of-thumbs” from an “easy-to-learn class”. Formally, we assume the class of weak hypotheses has a bounded VC dimension.

We focus on two main questions:

Local Statistics, Semidefinite Programming, and Community Detection

Prasad Raghavendra
University of California, Berkeley
May 4, 2020
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into k communities, and a graph is sampled conditional on a prescribed number of inter- and intra-community edges.

A Quantum Circuit Interpretation of Evaporating Black Hole Geometry

Ying Zhao
Member, School of Natural Sciences, Institute for Advanced Study
May 1, 2020
Abstract: When Alice shares thermofield double with Bob, her time evolution can make the wormhole grow. We identify different kinds of operations Alice can do as being responsible for the growth of different parts of spacetime and see how it fits together with subregion duality. With this, we give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double.

Latent Stochastic Differential Equations for Irregularly-Sampled Time Series

David Duvenaud
University of Toronto
April 30, 2020
Much real-world data is sampled at irregular intervals, but most time series models require regularly-sampled data. Continuous-time models address this problem, but until now only deterministic (ODE) models or linear-Gaussian models were efficiently trainable with millions of parameters. We construct a scalable algorithm for computing gradients of samples from stochastic differential equations (SDEs), and for gradient-based stochastic variational inference in function space, all with the use of adaptive black-box SDE solvers.

Eulerianity of Fourier coefficients of automorphic forms

Henrik Gustafsson
Member, School of Mathematics
April 30, 2020
The factorization of Fourier coefficients of automorphic forms plays an important role in a wide range of topics, from the study of L-functions to the interpretation of scattering amplitudes in string theory. In this talk I will present a transfer theorem which derives the Eulerianity of certain Fourier coefficients from that of another coefficient. I will also discuss some applications of this theorem to Fourier coefficients of automorphic forms in minimal and next-to-minimal representations.

A Framework for Quadratic Form Maximization over Convex Sets

Vijay Bhattiprolu
Member, School of Mathematics
April 28, 2020
We investigate the approximability of the following optimization problem, whose input is an
n-by-n matrix A and an origin symmetric convex set C that is given by a membership oracle:
"Maximize the quadratic form as x ranges over C."

This is a rich and expressive family of optimization problems; for different choices of forms A
and convex bodies C it includes a diverse range of interesting combinatorial and continuous
optimization problems. To name some examples, max-cut, Grothendieck's inequality, the

Ellipses of small eccentricity are determined by their Dirichlet (or, Neumann) spectra

Steven Morris Zelditch
Northwestern University
April 28, 2020
In 1965, M. Kac proved that discs were uniquely determined by their Dirichlet (or, Neumann) spectra. Until recently, disks were the only smooth plane domains known to be determined by their eigenvalues. Recently, H. Hezari and I proved that ellipses of small eccentricity are also determined uniquely by their Dirichlet (or, Neumann) spectra. The proof uses recent results of Avila, de Simoi, and Kaloshin, proving that nearly circular plane domains with rationally integrable billiards must be ellipses.