A new interpretation of the Leray number of a flag complex
Time and place
1 PM on Thursday, November 15th, 2012; NAC 6/113
Benjamin Steinberg (CCNY)
Abstract
The Leray number of a simplicial complex is a combinatorial invariant that was introduced in the first half of the twentieth century in the context of combinatorial geometry as an obstruction to representability of a simplicial complex as the nerve of a family of compact convex sets in Euclidean space. It was later considered by Hochster in the context of combinatorial commutative algebra as the Castelnuovo-Mumford regularity of the Stanley-Reisner ring of the simplicial complex.
We give in this talk a new interpretation of the Leray number of a flag complex as the global dimension of a certain finite dimensional algebra that we originally considered in the context of a Markov chain studied by Athanasiadis and Diaconis.
This is joint work with Stuart Margolis (Bar-Ilan University) and Franco Saliola (Universite de Quebec a Montreal).
