When: Sunday, June 4,
10am
Where: Schreiber 309
Speaker: Misha
Tyomkyn, Charles University
Title:
A New Approach for the Brown-Erdos-Sos Problem
The celebrated Brown-Erdos-Sos 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-Erdos-Sos conjecture up to an absolute additive constant.
Joint with Asaf Shapira.