Geometry and Cell Complexes

Invariants of Graphs, Their Associated Clique Complexes and Right-Angled Coxeter Groups

Michael Davis
The Ohio State University; Member, School of Mathematics
October 19, 2010

Associated to any simplicial graph there is a right-angled Coxeter group. Invariants of the Coxeter group such as its growth series or its weighted L^2 Betti numbers can be computed from the graph's clique complex (i.e., its flag complex).

Topology of Random Simplicial Complexes

Matthew Kahle
Institute for Advanced Study
October 5, 2010

In this talk I will overview two very different kinds of random simplicial complex, both of which could be considered higher-dimensional generalizations of the Erdos-Renyi random graph, and discuss what is known and not known about the expected topology of each. Some of this is joint work with Eric Babson and Chris Hoffman.