On October 1, 2019, Casey Tompkins at IBS discrete mathematics group presented a seminar talk on an extension of Turán’s theorem to hypergraphs. The title of his talk was “Extremal problems for Berge hypergraphs“.
Given a graph $G$, there are several natural hypergraph families one can define. Among the least restrictive is the family $BG$ of so-called Berge copies of the graph $G$. In this talk, we discuss Turán problems for families $BG$ in $r$-uniform hypergraphs for various graphs $G$. In particular, we are interested in general results in two settings: the case when $r$ is large and $G$ is any graph where this Turán number is shown to be eventually subquadratic, as well as the case when $G$ is a tree where several exact results can be obtained. The results in the first part are joint with Grósz and Methuku, and the second part with Győri, Salia and Zamora.
The IBS discrete mathematics group welcomes Dr. Casey Tompkins, a new research fellow at the IBS discrete mathematics group from September 1, 2019.
He received his Ph.D. from the Department of Mathematics at the Central European University in Budapest, Hungary in 2015 under the supervision of Prof. Gyula O. H. Katona.