数学大讲堂

Abstract

Ramsey Theory is an area of mathematics at the interface of logic, combinatorics and set theory, and had its inception in the work of logician F. P. Ramsey in the early twentieth century. The area is underpinned by the notion that in any sufficiently large "structure", there is a relatively large "uniform substructure". Erdős and Szekeres quantified these notions via Ramsey Numbers, which are a cornerstone of modern Ramsey Theory. In the last few years, there have been significant breakthroughs solving problems going back more than 80 years. In this talk, we will discuss the ideas and connections behind these advances, which include a blend of matrix theory, geometry, algebra, combinatorics and probability.

Biography

Jacques Verstraete is currently a full professor in the Department of Mathematics at UC San Diego in La Jolla, California. He received his PhD from Cambridge University in the Department of Pure Mathematics and Mathematical Statistics - DPMMS - under the supervision of Professor Andrew Thomason. He works in Extremal and Probabilistic Combinatorics and Ramsey Theory, and related areas of mathematics and theoretical computer science. Because of his outstanding research achievements, Jacques Verstraete was recently awarded the International Congress of Basic Science Frontiers of Science Award in Mathematics in 2024.