Research Interests

My interests lie in the realm of geometric group theory. More precisely, I am interested in topological properties of infinite groups, including classifying spaces, finiteness properties, homological stability and Bieri-Neumann-Strebel-Renz invariants. A typical tool I use is discrete Morse theory, which turns difficult global problems into easier local ones. Some groups of interest include braid groups, the extended family of Thompson's groups, groups of automorphisms of free groups and algebraic and arithmetic groups. Some relevant topological spaces include arc complexes, poset geometries, CAT(0) cube complexes, Outer/Auter space and buildings.

Using xkcd's word checker, here is a description of my research interests that uses only the 1000 most common words in the English language:

I study shapes and spaces, and try to understand groups that act on them. Some questions that I care about are whether a given group can act in a "nice" way on some "nice" space. The groups I like usually come with cool pictures and ways of viewing them. Some spaces I like are things like trees, and other flat shapes, and also "Outer space" and "buildings".