Research interests

I study phenomena in theoretical physics using rigorous mathematics. In particular, I'm trying to understand topological phases of matter and quantum field theory (QFT). I like to have a broad scope, both in mathematics and physics. My main focus during my PhD lies in understanding unitary topological field theories (TFT). I am also interested in symmetry-protected topological (SPT) phases.

My favorite way to describe QFT is by functorial quantum field theory. This framework was originally developed by Graeme Segal for conformal field theory and Michael Atiyah for topological field theory, but has since been generalized in multiple directions. In particular, functorial QFTs for metric-dependent theories have been defined by Stephan Stolz and my advisor Peter Teichner. Field theories that are invertible under tensor product (stacking) are called invertible. Invertible topological field theories are well-understood mathematically and provide a great tool to study SPT phases, as emphasized by Freed & Hopkins. Namely, the low energy effective field theory of (the continuum limit of) a QFT describing an invertible phase is often an invertible topological field theory.