Title：An Introduction to Recent Advances in Co-degree Turán Density of Hypergraphs

Abstract：We will introduce the fundamental relationship between codegree Turán density and uniform Turán density in 3-uniform hypergraphs. For a k-uniform hypergraph (or simply k-graph) F, the codegree Turán  density of F is the supremum over all f such that there exist arbitrarily large n-vertex F-free k-graphs H in which every (k − 1)-subset of V(H) is contained in at least fn edges. Recent research has demonstrated that whenever the codegree Turán density reaches zero for a given 3-uniform hypergraph, its uniform Turán density must necessarily also vanish. Building upon this foundation through the innovative concept of layered structures, Ding et al. establish a profound connection: for hypergraphs exhibiting such layered configurations, the disappearance of uniform Turán density guarantees the simultaneous vanishing of codegree Turán density. This discovery reveals a deep and intrinsic linkage between these two central density measures in hypergraph theory.

Speaker：Dr. Taijiang Jiang's research focuses on algebraic graph theory and extremal combinatorics, with a particular emphasis on extremal problems in hypergraphs.

Date：9:00am-11:30am 2025-6-19 (Wednesday).

Location of the report： Office 418, School of Mathematical Sciences

Organizer：School of Mathematical Science

Inviter：Qiang Sun

Students and teachers who are interested in graph theory are welcome.