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Computation & Combinatorics of Sections of Polytopes
Student-Run Research| Speaker: | Anouk Brose |
| Location: | 2112 MSB |
| Start time: | Thu, May 7 2026, 11:00AM |
Description
My research focuses on studying sections of polytopes from the point of view of 1. computing them, 2. counting them and 3. reconstructing them. I have been studying these questions both for “any polytope”, and for lattice polytopes (i.e. those whose vertices have integer coordinates). For example: Can we compute a “best” section of a polytope? Here “best" could mean maximal volume, maximal number of lattice points, maximal number of vertices, … How many “best” sections does any given polytope have? Can we reconstruct combinatorial data of a polytope from combinatorial data of its slices? I will present some results on my first projects and highlight future research goals.