PIMS- UVic Discrete Math Seminar:Bhargav Narayanan

Nati Linial raised the following basic problem in 2006: given a k-dimensional simplicial complex S, how many facets can a k-complex on n vertices have if it contains no topological copy of S? This is a beautiful and natural question, but results in low dimensions apart (k ≤ 2), very little was previously known. In this talk, I’ll provide an answer in all dimensions and take the scenic route to the answer, surveying many natural problems about simplicial complexes along the way.