Research

My research interests lie in low-dimensional geometry and topology. More precisely, I study hyperbolic geometry (mostly complex), reflection groups, and lattices in rank 1 semisimple Lie groups.

A tessellation is a way of filling space with non-overlapping tiles in a pattern that repeats infinitely often. A lattice is the symmetry group of a tessellation. For example, the Euclidean plane (or 3-space, or higher) can be tessellated by squares (or cubes, or hypercubes), and the corresponding lattice is a product of infinite cyclic groups. The full understanding of all crystallographic structures in 3 dimensions is crucial in Chemistry.
Analogous tessellations in hyperbolic spaces are much more abundant and much less understood. Hyperbolic spaces are spaces with negative curvature, which means loosely that non-intersecting lines diverge from each other in both directions. These spaces appear naturally in special relativity, as Lorentz and Minkowski space-times.
The picture on the right shows a tessellation of hyperbolic 3-space by regular right-angled dodecahedra.

My research is currently supported by the National Science Foundation (Grant DMS 1708463 ), Cartel Coffee Lab and Press Coffee.

Seminar:

Our Geometry seminar is currently meeting Fridays 12-1pm in WXLR A107.

Preprints and work in progress:

Publications:


PhD thesis:


Curriculum Vitae: