I am an Associate Professor in the Department of Mathematical Sciences at Carnegie Mellon University. Before joining CMU I was an H.C. Wang Assistant Professor at Cornell University and a Ph.D. student at TU Berlin. During the Fall semester 2017 I was at MSRI in Berkeley. During the 2021/22 academic year I was visiting Freie Universität Berlin.
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I am running a Research Experience for Undergraduates on Geometry and Topology in a Discrete Setting during the summer of 2024.
My work develops geometric and topological methods to solve problems both of a geometric flavor and further afield. For the latter, I "geometrize" problems that may benefit from topological techniques, which are particularly well-suited to keep track of global phenomena. Among the topological methods that I develop are existence and nonexistence results for equivariant maps and embeddings of topological spaces as well as fixed-point theorems. Beyond algebraic and geometric topology, I apply these tools to a diverse set of problems, such as chromatic numbers of hypergraphs in combinatorics, fair division results in game theory and convex geometry, the large-scale structure of point sets in computational topology, and polytope theory. Within geometric topology, in addition to the theory of embeddings, I work on manifold triangulations, inscribability problems, and metric geometry.