Combinatorics Seminar - Alan Lew

17:15-18:00

Speaker: Alan Lew

Title: Leray numbers of tolerance complexes

Abstract: In  this  talk  we  will  discuss  the  Leray  and  collapsibility  numbers of  a  simplicial  complex K,  and  their  role  in Helly-type  theorems  in combinatorial geometry.  The Leray number is, roughly speaking, the hereditary homological dimension of K, while the collapsibility number captures the complexity of dismantling K by sequentially removing free faces from K.

Following the formal definition of these parameters and their connection to the combinatorics of convex sets, we will introduce the construction of the “tolerance complex” of a complex K.  We will explain its relation to a tolerant version of Helly’s theorem due to Montejano and Oliveros and present new results on the Leray numbers of these complexes.
The talk is based on joint work with Minki Kim.