Research:
I mainly focus on trying to transfer ideas between low dimensional topology and number theory. Most recently I have been working on a framework for arithmetic TQFTs, analogies of mapping class groups and Teichmuller theory for p-­adic fields, understanding links in 3-manifolds which behave like prime numbers, and profinite covers of 3­-manifolds.
I am also very interested in questions related to anabelian geometry and p-adic hodge theory.