Places
- Since 08/24 I’m back in Cambridge as a Research Fellow at Gonville & Caius College, Cambridge.
- From 08/22 till 07/24 I was a postdoc at Københavns Universitetet.
- In 2021/22 was a Research Fellow at Gonville & Caius College, Cambridge.
- Before that I was doing a PhD with Ulrike Tillmann.
- Even before that I did my undergrad in Freiburg.
Interests
I’m interesting in studying moduli spaces of manifolds using homotopy theory and higher category theory. This has led to the following projects: (See Projects for the associated papers.)
- My thesis was about classifying spaces of low-dimensional bordism categories. This involved computing classifying spaces of the discrete one and two-dimensional bordism category and developing tools for constructing homotopy fiber sequences of classifying spaces.
- I’m currently studying algebras over the surface modular operad (aka non-extended 2d TFTs or modular functors) with values in infinity-categories. When restricting to invertible algebras, this gives a spectral sequence that for example implies that the 14th rational cohomology group of the genus 5 mapping class group has rank at most 2.
- I’m working with Shaul Barkan on a theory of infinity-properads, cyclic operads, and modular operads, that has a good theory of algebras while at the same time having effective formulas for relative-free operads. This for instance allows us to describe the “free symmetric monoidal infinity category on a commutative Frobenius algebra”. We also plan to use this to compute the stable homology of diffeomorphism groups of certain 3-manifolds.
- With Rachael Boyd and Corey Bregman I’m studying moduli spaces of reducible 3-manifolds. We use idea motivated by modular operads to prove Kontsevich’s conjecture about the finiteness of moduli spaces for oriented 3-manifolds with boundary.
I’m also interested in bordism categories and TFTs more generally, diffeomorphisms groups, K-theory, functor calculus and anything vaguely related to homotopy theory or manifolds.