Florian Frick
Associate Professor
Address:
7109 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
P: 412-268-3781
Education
Ph.D., Technische Universität Berlin and Berlin Mathematical School
Postdoctoral Appointments:
- Cornell University
- Mathematical Sciences Research Institute
Awards
- NSF CAREER Award
Research
My research "geometrizes" problems that benefit from understanding global information. Topology and geometry are suitable tools to organize non-local phenomena and detect global obstructions. Sometimes these problems are of geometric nature themselves, such as understanding the intersection combinatorics of convex hulls in Euclidean space, inscribing geometric shapes into curves, partitioning a point set by hyperplanes, or reconstructing the shape that a data set was sampled from. I also apply geometric-topological methods further afield. Examples include chromatic numbers of hypergraphs and extremal combinatorics, fair division problems in game theory, and packing and covering inequalities in combinatorial settings.
Select Publications
Frick, F. (2018). Chromatic numbers of stable Kneser hypergraphs via topological Tverberg-type theorems. Int. Math. Res. Not. IMRN, to appear.
Frick, F. and Zerbib, S. (2018). Colorful coverings of polytopes and piercing numbers of colorful d-intervals. Combinatorica, to appear.Frick, F., Houston-Edwards, K. and Meunier, F. (2018). Achieving rental harmony with a secretive roommate. Amer. Math. Monthly, to appear.
Blagojević, P., Frick, F. and Ziegler, G. (2018). Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints. J. Europ. Math. Soc. (JEMS), to appear.
Blagojević, P., Frick, F., Haase, A. and Ziegler, G. (2018). Topology of the Grünbaum−Hadwiger−Ramos hyperplane mass partition problem. Trans. Amer. Math. Soc. 370 (10), 6795−6824.
Frick, F. (2017). Intersection patterns of finite sets and of convex sets. Proc. Amer. Math. Soc. 145 (7), 2827−2842.
Adamaszek, M., Frick, F. and Vakili, A. (2017). On homotopy types of Euclidean Rips complexes. Discrete Comput. Geom. 58 (3), 526−542.
Blagojević, P., Frick, F., Haase, A. and Ziegler, G. (2016). Hyperplane mass partitions via relative equivariant obstruction theory. Documenta Math. 21, 735−771.
Adamaszek, M., Adams, H., Frick, F., Peterson, C. and Previte-Johnson, C. (2016). Nerve complexes of circular arcs. Discrete Comput. Geom. 56 (2), 251−273.
Blagojević, P., Frick, F. and Ziegler, G. (2014). Tverberg plus constraints. Bull. London Math. Soc. 46, 953−967.