I am a mathematician at The Ohio State University. My research is in the area of group theory and has ramifications into algebraic and geometric combinatorics, homological algebra and category theory.
More specifically, I study combinatorial structures related to group actions, such as buildings and group geometries.
Among the projects that I have been working on, I have focused on subgroup complexes, simplicial complexes which arise in a natural way from the group structure, and their properties such as topological invariants and the connections to the representation theory of the underlying group.
I have also done research on fusion and linking systems, these are categorical objects that generalize the notion of the group. In particular, I have studied fusion systems with associated combinatorial structures called chamber systems.
In a slightly different direction, I have a keen interest in computer science, and mainly in how to apply algebraic techniques to data science and neural networks.
Prior to becoming a mathematician I worked as a research physicist, in the areas of general relativity and gravitation.