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 application of homotopy-theoretical methods to explore questions about manifolds.
On the other hand, within matroid theory, the current focus of my research is to study matroid invariants (e.g., the Tutte polynomial) via the machinery of cut-and-paste K-theory, a novel variant of higher algebraic K-theory that provides a framework to study decompositions of combinatorial and geometric objects through the lens of homotopy theory.
Publications and Preprints
- The homotopy type of the topological cobordism category, with Alexander Kupers. Documenta Mathematica 27, 2107-2182 (2022).
- The homotopy type of the PL cobordism category. I. To appear in Algebraic & Geometric Topology.
- The homotopy type of the PL cobordism category. II. To appear in Algebraic & Geometric Topology.
- Realizing the Tutte polynomial as a cut-and-paste K-theoretic invariant. arXiv:2501.12250.
In Preparation
- Symmetric monoidal categories of matroids and cut-and-paste K-theory.
- The magnitude of a matroid.