University of Illinois at Urbana-Champaign, Department of Mathematics

Currently, my work focuses on the interplay between geometric group theory and number theory:

I study arithmetic properties of integer matrix groups such as various monodromy groups and hyperbolic reflection groups. This usually involves combining arithmetic tools with the geometry inherent to these groups. More recently these interests have led me to investigate how generic certain properties of such groups are.

See this article in the American Scientist, or, if you speak French, this interview in the French science magazine La Recherche for an overview of the kinds of problems I considered in my thesis.

Publications and Preprints:

Unpublished Notes: