Research interests

Most broadly, I study combinatorics and group theory.

One area that I work in is the combinatorial topology of partially ordered sets, or posets. Some posets of particular interest to me come from group theory. Examples include the lattice of all subgroups of a finite group, of all cosets of a finite group, of all normal or subnormal subgroups of a finite group, and so forth. Combinatorial properties such as shellability often have nice characterizations in terms of the group theory.

Another interesting area is the topology of independence complexes. The simplest version of this is to start with a graph, and let the simplicial complex have the same vertex set as the graph, and faces the subsets containing no edge. One can then prove theorems about the interaction between the graph theory and the topology of this complex.

See my papers in progress for an up-to-date summary of what I've been working on lately, or my published papers for a more complete survey of my interests.

I also have some mathematical software, including Gap.app, available in the Programming section of my website.

The subgroup lattice of S_4
L(S₄), the subgroup lattice of the symmetric group on 4 letters.
Diagram created with GAP and XGAP.