기초과학연구원 이산수학그룹
On February 6, 2024, Ander Lamaison from the IBS Extremal Combinatorics and Probability Group gave a talk at the Discrete Math Seminar on the uniform Turán density of a hypergraph. The title of his talk is “Uniform Turán density beyond 3-graphs“.
The IBS Discrete Mathematics Group welcomes Zichao Dong and Ander Lamaison, two new research fellows at the IBS Extremal Combinatorics and Probability Group and welcomes Qiang Zhou, a new visiting student of the IBS Extremal Combinatorics and Probability Group.
Dr. Zichao Dong received his Ph.D. from the Carnegie Mellon University in 2023 under the supervision of Prof. Boris Bukh.
Dr. Ander Lamaison received his Ph.D. from the Freie Universität Berlin in 2021 under the supervision of Prof. Tibor Szabó.
Qiang Zhou is a graduate student from the Chinese Academy of Sciences. He will stay until the end of June 2024.
The uniform Turán density $\pi_u(F)$ of a hypergraph $F$, introduced by Erdős and Sós, is the smallest value of $d$ such that any hypergraph $H$ where all linear-sized subsets of vertices of $H$ have density greater than $d$ contains $F$ as a subgraph. Over the past few years the value of $\pi_u(F)$ was determined for several classes of 3-graphs, but no nonzero value of $\pi_u(F)$ has been found for $r$-graphs with $r>3$. In this talk we show the existence of $r$-graphs $F$ with $\pi_u(F)={r \choose 2}^{-{r \choose 2}}$, which we conjecture is minimum possible. Joint work with Frederik Garbe, Daniel Il’kovic, Dan Král’ and Filip Kučerák.