Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium

Thursday, February 29, 2024 at 4:30pm

Building 2, 190
182 MEMORIAL DR, Cambridge, MA 02139

Speaker: Julian Sahasrabudhe (Cambridge)

Title: Diagonal Ramsey numbers and high dimensional geometry

Abstract:

Let R(k) be the kth diagonal Ramsey number: that is, the smallest n for which every two-colouring of the edges of the complete graph on n vertices contains a monochromatic complete graph on k vertices. Since their introduction by Ramsey in the 1930s, these numbers have become a central topic in combinatorics and have inspired many beautiful advances in the intervening years, including the development of the probabilistic method and pseudo-random graphs.

In recent work with Marcelo Campos, Simon Griffiths and Rob Morris, the speaker showed that  R(k) < (4-c)^k, for some absolute constant c > 0, which was the first exponential improvement over the bound of Erdős and Szekeres, proved in 1935. In this talk I will discuss the proof and a further connection with a conjecture on random variables that take values in high dimensional space. If true, this conjecture has further implications for our understanding of the Ramsey numbers.

Department
Department of Mathematics
Contact Email

kristims@mit.edu

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