588 Malott Hall
Ph.D. (2015) Technische Universität Berlin and Berlin Mathematical School
Topological combinatorics and convex geometry
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.
Hyperplane mass partitions via relative equivariant obstruction theory (with Pavle Blagojevic, Albert Haase, and Günter M. Ziegler), Documenta Mathematica, to appear, arXiv:1509.02959.
Counterexamples to the topological Tverberg conjecture, Oberwolfach Reports 12 (1) (2015), 318-321, arXiv:1502.00947.
Nerve complexes of circular arcs (with Michal Adamaszek, Henry Adams, Chris Peterson, and Corrine Previte-Johnson), Discrete Comput. Geom., to appear, arXiv:1410.4336.
Tverberg plus constraints (with Pavle V. M. Blagojevic and Günter M. Ziegler), Bull. Lond. Math. Soc. 46 (2014), no. 5, 953-967.