My research focuses on applying topology to combinatorial and discrete-geometric problems. This includes measure partition problems, zero-sum problems, the embeddability of cell complexes into Euclidean space and more generally Tverberg-type incidence theorems, which are concerned with the intersection pattern of faces in a simplicial complex when mapped to Euclidean space. Oftentimes this topological approach yields extensions of theorems from convex geometry to a merely continuous setting. Perhaps surprisingly number-theoretic condition play a major role in determining which convex geometric results hold also in the more general topological sense. In addition, I am interested in the closely related topics of manifold triangulations and polytope theory.
