Schedule

Schedule 2022 2023

Upcoming talks in The Vinberg Lecture Series

Jan 26, 2022
Wednesday
10.30
New York
UTC -5
Bjorn Poonen MIT, USA
Undecidability in number theory

Hilbert's tenth problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be. The second half of the lecture will explore some of the techniques from arithmetic geometry that have been used towards answering this question and the related question for the ring of integers of a number field.

Feb 23, 2022
Wednesday
10.30
New York
UTC -5
Maxim Kontsevich IHES, France
Introduction to wall-crossing

TBA

Mar 23, 2022
Wednesday
10.30
New York
UTC -4
David Fisher Indiana University Bloomington, USA
Arithmeticity, superrigidity, and totally geodesic submanifolds

Arithmeticity of locally symmetric spaces is an old and important area of study in which Vinberg proved some central results. I will discuss the history of the area, some open questions and then focus on recent joint work with Bader, Miller and Stover. We prove that non-arithmetic real and complex hyperbolic manifolds cannot have infinitely many maximal totally geodesic submanifolds.

Apr 13, 2022
Wednesday
10.30
New York
UTC -5
David Kazhdan Hebrew University, Israel
On the Langlands correspondence for curves over local fields

On results and (mostly) conjectures on automorphic functions on moduli spaces of 2-dimensional vector bundles on curves over local fields

May 4, 2022
Wednesday

12.30

New York
UTC -5
Igor Pak UCLA, USA
Combinatorial inequalities

In the ocean of combinatorial inequalities, two islands are especially difficult. First, Mason's conjectures say that the number of forests in a graph with k edges is log-concave. More generally, the number of independent sets of size k in a matroid is log-concave. Versions of these results were established just recently, in a remarkable series of papers by Huh and others, inspired by algebro-geometric considerations.

Second, Stanley's inequality for the numbers of linear extensions of a poset with value k at a given poset element, is log-concave. This was originally conjectured by Chung, Fishburn and Graham, and famously proved by Stanley in 1981 using the Alexandrov–Fenchel inequalities in convex geometry. No direct combinatorial proof for either result is known. Why not?

In the first part of the talk we will survey a number of combinatorial inequalities. We then present a new framework of combinatorial atlas which allows one to give elementary proofs of the two results above, and extend them in several directions. This talk is aimed at the general audience.

Date TBA
Wednesday
10.30
New York
UTC -5
Victor Kac MIT, USA
Exceptional de Rham complexes
Date TBA
Wednesday
10.30
New York
UTC -5
Akshay Venkatesh IAS Princeton, USA
TBA
17.08.2021
Tuesday
19.00
UTC +3
Avi Wigderson IAS, Princeton
Optimization, Complexity and Math (or, can we prove P ≠ NP using gradient descent)

This talk aims to summarize the status and goals of a broad research project. The main messages of this project are summarized below; I plan to describe, through examples, many of the concepts they refer to, and the evolution of ideas leading to them. No special background is assumed.

  1. We extend some basic algorithms of convex optimization from Euclidean space to the far more general setting of Riemannian manifolds, capturing the symmetries of non-commutative group actions. The main tools for analyzing these algorithms combine central results from invariant and representation theory.
  2. One main motivation for studying these problems and algorithms comes from algebraic complexity theory, especially attempts to separate Valiant’s algebraic analogs of the P and NP. Symmetries and group actions play a key role in these attempts.
  3. The new algorithms give exponential (or better) improvements in run-time for solving algorithmic many specific problems across CS, Math and Physics. In particular, in algebra (testing rational identities in non-commutative variables), in analysis (testing the feasibility and tightness of Brascamp-Lieb inequalities), in quantum information theory (to the quantum marginals problem), optimization (testing membership in “moment polytopes”), and others. This work exposes old and new connections between these diverse areas.
Meeting ID: 28846929 zoom-link
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