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.
Here is my research statement (from Sept 2016, will likely not be updated anytime soon).
My coauthors and collaborators:
Justin Tatch Moore
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: