Talk information

Date: Sunday, June 4, 2023
Time: 10:10–11:00
Place: Schreiber 309
Speaker: Misha Tyomkyn (Charles University)
Title: A new approach for the Brown–Erdős–Sós problem

Abstract:

The celebrated Brown–Erdős–Sós conjecture states that for every fixed $e$, every $3$-uniform hypergraph with $\Omega(n^2)$ edges contains $e$ edges spanned by $e+3$ vertices. Up to this date all the approaches towards resolving this problem relied on highly involved applications of the hypergraph regularity method, and yet they supplied only approximate versions of the conjecture, producing $e$ edges spanned by $e+O(\log e/\log \log e)$ vertices.

We shall describe a completely different approach, which reduces the problem to a variant of another well-known conjecture in extremal graph theory. A resolution of the latter would resolve the Brown–Erdős–Sós conjecture up to an absolute additive constant.

Joint with Asaf Shapira.