vinberg.combgeo.orgThe Vinberg Lecture – Distinguished Online Lecture Series

The Vinberg Lecture Distinguished Online Lecture Series Toggle mobile menu About Schedule Archive Organizers Search for: The Vinberg Lecture The Vinberg Distinguished Lecture Series aims at bringing together all mathematicians interested in wide dissemination of ideas from various domains of pure and applied mathematics. During his lifetime, È. B. Vinberg has made outstanding contributions to many branches of mathematics, such as Lie groups and algebraic groups, representation theory, invariant theory, hyperbolic geometry, automorphic forms, and discrete subgroups of Lie groups. We hope to carry on Vinberg’s legacy and bring together a wider community of mathematicians interested in the above mentioned domains as well as other fields of study. Format A usual lecture is about 90 minutes long: the first part is a survey talk, and the second part is aimed at experts. There is a short break (about 10 minutes) in between. If you want to make a talk or make a suggestion, please contact the organisers at email vinberg-lecture@phystech.com . Time & date In order to obtain the correct time and date of forthcoming talks at your geographic location, please consult our schedule at ResearchSeminars.org Zoom & recordings The Vinberg Lecture talks are held in Zoom. Please register here to receive a Zoom link. All recorded videos will appear in YouTube Playlist Upcoming talks Date TBA Wednesday 10.30 New York UTC -5 Victor Kac MIT, USA Exceptional de Rham complexes Abstract Zoom info ► Watch video Go to the page ➝ 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. 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. 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. 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 Password: in open or as a puzzle Date TBA Wednesday 10.30 New York UTC -5 Akshay Venkatesh IAS Princeton, USA TBA Abstract Zoom info ► Watch video Go to the page ➝ 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. 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. 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. 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 Password: in open or as a puzzle Past Talks: Spring 2022 See other scheduled talks May 4, 2022 Wednesday 12.30 New York UTC -5 Igor Pak UCLA, USA Combinatorial inequalities Abstract Zoom info ► Watch video Go to the page ➝ 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. Apr 13, 2022 Wednesday 10.30 New York UTC -5 David Kazhdan Hebrew University, Israel On the Langlands correspondence for curves over local fields Abstract Zoom info ► Watch video Go to the page ➝ On results and (mostly) conjectures on automorphic functions on moduli spaces of 2-dimensional vector bundles on curves over local fields. Past talks Feb 23, 2022 Wednesday 10.30 New York UTC -5 Maxim Kontsevich IHES, France Introduction to wall-crossing Abstract Zoom info ► Watch video Go to the page ➝ Wall-crossing structures appeared several years ago in several mathematical contexts, including cluster algebras and theory of generalized Donaldson-Thomas invariants. In my lecture I will describe the general formalism based on a graded Lie algebra and an additive map from the grading lattice to an oriented plane ("central charge"). A geometric example of a wall-crossing structure comes from theory of translation surfaces. The number of saddle connections in a given homology class is an integer-valued function on the parameter space (moduli space of abelian or quadratic differentials), which jumps along certain walls. The whole theory can be made totally explicit in this case. Also, I’ll talk about another closely related example, which can be dubbed a "holomorphic Morse-Novikov theory". Mar 23, 2022 Wednesday 10.30 New York UTC -4 David Fisher Indiana University Bloomington, USA Arithmeticity, superrigidity, and totally geodesic submanifolds Abstract Zoom info ► Watch video Go to the page ➝ 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. Jan 26, 2022 Wednesday 10.30 New York UTC -5 Bjorn Poonen MIT, USA Undecidability in number theory Abstract Zoom info ► Watch video Go to the page ➝ 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...