Chiara Meroni: Cube slice recovery

Abstract: Hyperplane sections of cubes form a rich and surprisingly intricate class of polytopes. I will begin by discussing recent work with Marie-Charlotte Brandenburg on the computational classification of the combinatorial types of slices of cubes up to dimension six or seven. Motivated by the patterns revealed by this classification, I will then focus on a reconstruction problem for cube slices: whether the full combinatorial type of such a section is determined by its vertex-edge graph. The talk will discuss this question and possible generalizations, based on an ongoing work with Marie-Charlotte Brandenburg, Julie Curtis, Chiara Giardino, and Arnau Padrol.