GEOMETRY AND CELL COMPLEXES
Geometry and Cell Complexes
The d-divisible partition lattice is the collection of all partitions of an n-element set where each block size is divisible by d. Stanley showed that the Mobius
we will describe various models of sparse and planar graphs and the associated distributions of eigenvalues (and eigenvalue spacings) which come up. The talk will be light on theorems, and heavy on experimental data.
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).
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.