AMR-RMA
Recent Mathematical Advances Distinguished Lecture Series
December 5, 2024
8:00 AM (Los Angeles), 11:00 AM (Montreal, New York), 4:00 PM (London) 5:00 PM (Madrid, Paris) 6:00 PM (Tel-Aviv)
Alexander Razborov
University of Chicago & Steklov Institute
TITLE: Continuous Combinatorics
Abstract
Discretization, or replacing continuous objects with their finite approximations, is a common technique in mathematics. In this talk I will focus on several related efforts to go in the opposite direction, namely pretending that “very large” combinatorial objects are actually infinite and studying the resulting limit structures from different perspectives.
Upon briefly reviewing the basics of the theory (graphons and flag algebras), I will report on some more recent developments. Those, time permitting, will include applications to the theory of quasi-randomness and to machine learning. This last part is based on joint work with L. Coregliano and on another paper by Coregliano and Malliaris.
About the speaker
Alexander Razborov, the Andrew McLeish Distinguished Service Professor at the University of Chicago, made major contributions to several fields of mathematics and computer science. He introduced a number of fundamental notions including the Makanin-Razborov diagrams used in the analysis of equations in groups; natural proofs (with Rudich) — a class of strategies used to prove fundamental lower bounds in computational complexity; the flag algebras, which became an important computational tool in graph theory. Razborov honors include Nevanlinna Prize (1990) and Gödel Prize (2007). He delivered invited lectures at the International Congress of Mathematicians in 1986 and the European Congress of Mathematics in 2021. Razborov is a member of the Academia Europaea since
1993, a Corresponding member of the Russian Academy of Sciences since 2000, and a member of the American Academy of Arts and Sciences since 2020.
Learn More About This Topic
- L. Lovasz, Large Networks and Graph Limits, AMS, 2012.
- A. Razborov, What is a Flag Algebra?, Notices of the AMS, 60(10): 1324-1327, 2013.
- L. Coregliano, A. Razborov, Natural Quasirandom Properties, in Random Structures and Algorithms, Vol. 63, 2023, No 3, 624-688.
- L. Coregliano, M. Malliaris, High-arity PAC learning via exchangeability, https://arxiv.org/abs/2402.14294.