When: Sunday, May 16, 10am
Where: Schreiber 309
Speaker: Chong Shangguan, Shandong University, China
Title: On Two Extremal Hypergraph Problems of Brown, Erdos
and Sos
An $r$-graph is called $(v,e)$-free if the union of any $e$ distinct edges of it contains at least $v+1$ vertices. Let $f_r(n,v,e)$ denote the maximum number of edges of a $(v,e)$-free $r$-graph on $n$ vertices. The study of the function $f_r(n,v,e)$ was initiated by Brown, Erdos and Sos in 1973. In this talk we will introduce our recent progress on the following two interesting conjectures.
Conjecture 1: For all fixed $e \ge 3$ and $r\ge 3$, we have $n^{2-o(1)} \le f_r(n,er-2e+3,e)=o(n^2)$.
Conjecture 2: For all fixed $e\ge 3$ and $r\ge 3$, the limit $\lim f_r(n,er-2e+2,e)/n^{2}$ always exist.
Joint works with Gennian Ge and Itzhak Tamo