
Research InterestsMy 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 BieriNeumannStrebelRenz 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: Peter Abramenko Jim Belk Collin Bleak Matt Brin KaiUwe Bux Martin Fluch Andy Heald Judy Holdener Martin Kassabov Lee Kennard Marco Marschler Robert McEwen Justin Tatch Moore Mark Pearson Lucas Sabalka Rachel Skipper Marco Varisco Stefan Witzel 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: 