A geometric transversal to a family of convex sets in the d-dimensional Euclidean space is an affine flat that intersects the members of the family. While there is a well-developed theory concerning 0-dimensional transversals (« intersection patterns of convex sets’’) with deep connections to algebraic, enumerative, geometric, and topological combinatorics, much less is known when it comes to higher-dimensional transversals. In this talk, I will give an introduction to this field of study and highlight some new and old results and open problems. This is based in part on joint work with Otfried Cheong and Xavier Goaoc.
Seminar room 4B125 (Copernic building)
5 Boulevard Descartes 77420 Champs-sur-Marne