Combinatorics Seminar
John Steenbergen
UIC
From Graphs to Simplicial Complexes: Isoperimetric Constants, Random Walks, and the Hodge Laplacian
Abstract: Isoperimetric constants and random walks have played an important role in the study of spectral graph theory and its applications, like clustering and partially-labelled classification. In this talk, we present new types of isoperimetric constants and random walks on simplicial complexes which generalize to higher dimensions their classical counterparts on graphs. Of particular interest is how these relate to the spectrum of the combinatorial Hodge Laplacian. Various results will be presented which shed light on the spectral gap and what it means for a simplicial complex to "almost" have a nontrivial homology class. Higher-dimensional analogues of clustering and partially-labelled classification will also be discussed.
Wednesday March 19, 2014 at 3:00 PM in SEO 427