Mingyuan Rong, The codegree Turán density of tight cycles

The codegree Turán density γ(F) of a k-uniform hypergraph F is the smallest γ ≥ 0 with the following property: if every set of k−1 vertices in an n-vertex k-uniform hypergraph H lies in at least (γ+o(1))n edges, then H contains a copy of F for all sufficiently large n. Piga, Sanhueza-Matamala, and Schacht proved that this density is 1/3 for all sufficiently long 3-uniform tight cycles whose lengths are not divisible by 3. In this talk, I will discuss extensions of this result to higher uniformities, where we determine the codegree Turán density of tight cycles for a broad range of cycle lengths. I will explain the structural characterization underlying the upper bounds and the constructions used for the lower bounds. This is joint work with Jie Ma.