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...
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
function of the d-divisible partition lattice is given (up to a
sign) by the number...
The cd-index is a noncommutative polynomial which compactly
encodes the flag vector data of a polytope, and more generally, of
a regular cell complex. Ehrenborg and Readdy discovered the
cd-index has an inherent coalgebraic structure which...
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).
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.
Polycrystalline materials, such as metals, ceramics and
geological materials, are aggregates of single-crystal grains that
are held together by highly defective boundaries. The structure of
grain boundaries is...
