My research agenda has two prominent directions: algebraic topology and matroid theory.
As an algebraic topologist, I enjoy studying spaces of manifolds and cobordism categories. A recurring theme in this direction is the use of homotopy-theoretical methods to tackle problems related to manifolds.
On the other hand, within matroid theory, I’m currently studying different ways of defining metrics on matroids. My ultimate goal in this direction is to obtain new matroid invariants. For example, once a metric is in place, one can use the machinery of magnitudes (as developed by Leinster et al.) to generate novel invariants for matroids.
Preprints & Publications
- The homotopy type of the topological cobordism category, with Alexander Kupers. To appear in Documenta Mathematica.
- The homotopy type of the PL cobordism category. I. Submitted to Algebraic & Geometric Topology.
- The homotopy type of the PL cobordism category. II. Submitted to Algebraic & Geometric Topology.
In Preparation
- The magnitude of a matroid, with Gary Gordon.