马杰 , 本杰明·苏达科夫 , 许睿捷

Bjarne Schülke

2026年11月10日 17:05 至 18:15

Online

Zoom 787 662 9899 (BIMSA)

Since suggested by Turán in 1941, determining the Turán density of hypergraphs has been a notoriously difficult problem at the center of extremal combinatorics. Roughly speaking, the Turán density $\pi(F)$ of a hypergraph $F$ is the threshold of the edge density above which large hypergraphs are guaranteed to contain a copy of $F$. The codegree Turán density $\gamma(F)$ is a variant that was introduced by Mubayi and Zhao roughly 20 years ago. The minimum codegree of a $k$-graph is the minimum number of edges that a $k-1$-subset of vertices is contained in. The codegree Turán density is the minimum $d\in[0,1]$ such that every sufficiently large hypergraph $H$ with minimum codegree at least $(d+o(1))|V(H)|$ must contain a copy of $F$. In this talk, we compare the behaviour of Turán densities with that of codegree Turán densities. In particular, we discuss results regarding accumulation points of Turán densities and codegree Turán densities and the characterisations of 3-graphs with (codegree) Turán density zero.

Based on several joint works with different subsets of Conlon, Lamaison, Li, Liu, Liu, King, Piga, Sales, Sun, Wang, Wu, Yang, and Zhang.

Bjarne Schülke is a Young Scientist Fellow in the Extremal Combinatorics and Probability Group at the Institute for Basic Science in South Korea. His research focuses on extremal combinatorics, particularly the hypergraph Turán problem, spanning structures in graphs and hypergraphs, bootstrap percolation, and extremal set theory. From 2018 to 2021 he was a PhD student of Christian Reiher and Mathias Schacht at the University of Hamburg. From 2021 to 2024, he was a Harry Bateman Research Instructor at the California Institute of Technology, working with David Conlon. Since 2024 he is a Young Scientist Fellow at the Institute for Basic Science.