The ACO Seminar (2024–2025)

The homeomorph Turán problem is the extremal hypergraph problem to determine the maximum number of facets in a pure d-dimensional simplicial complex on n vertices that does not contain a subcomplex homeomorphic to some fixed d-dimensional topological space. The d = 1 case of this problem (i.e. subdivisions of a fixed graph) was settled decades ago by Mader, and in the last few years there has been substantial progress for the d = 2 case by many different researchers. In this talk I will outline some of this recent progress and then turn attention to joint work with Marta Pavelka in which we study the homeomorph Turán problem for the d-dimensional sphere and tie the problem to an important enumeration question of Gromov.