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Research interests
Most broadly, I study combinatorics and group theory.More especially, I study 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.
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.
L(S4), the subgroup lattice of the symmetric group on 4 letters.
Diagram created with GAP and XGAP.