Geometry Seminar

Date: February 26, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Ron Rosenthal, Technion

Title: Random Steiner complexes

Abstract: We will discuss a new model for random d-dimensional simplicial complexes, for d ≥ 2, whose (d − 1)-cells have bounded degrees. The construction relies on Keevash's results on the existence of Steiner systems which are generalizations of regular graphs. We will show that with high probability, complexes sampled according to this model are high-dimensional expanders. This gives a full solution to a question raised by Dotterrer and Kahle, which was solved in the two-dimensional case by Lubotzky and Meshulam. In addition, we will discuss the limits of their spectral measures and their relation to the spectral measure of certain high-dimensional regular trees. Based on a joint work with Alex Lubotzky and Zur Luria and a work in progress with Yuval Peled.