Session II.6 - Computational Algebraic Geometry
Thursday, June 15, 17:00 ~ 17:30
Hyperplane sections of polytopes
Chiara Meroni
MPI Leipzig, Germany - This email address is being protected from spambots. You need JavaScript enabled to view it.
We obtain a parametric, semialgebraic description of properties of the hyperplane sections of a polytope. Using this structure, we provide algorithms for the optimization of several combinatorial and metric properties over all hyperplane slices of a polytope. We report on their computational complexity, and explore some connections to constructions and problems in combinatorics and convex geometry.
Joint work with Marie-Charlotte Brandenburg (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) and Jesús A. De Loera (University of California, Davis, USA).