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Lattice Diameter of Lattice Polygons
Student-Run Research Seminar| Speaker: | Anouk Brose, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Feb 19 2025, 1:10PM |
This talk is about discrete and combinatorial properties of slices of polytopes. A slice of a polytope is the intersection of the polytope with an affine hyperplane. Combinatorially, we are interested in the f-vector of slices, e.g. the number of vertices in different slices of a given polytope. We give bounds on the number of vertices in slices, and characterize sequences of the number of vertices that can appear in slices of fixed 3-dimensional polytopes, or hypercubes. Further we study lattice points in slices of lattice polytopes. The main result is a polynomial-time algorithm in dimension 2, that computes the line of a lattice polygon which contains maximally many lattice points, i.e. computes the lattice diameter. This is joint work with Jesús de Loera, Gyivan Lopez, and Antonio Torres.
Free pizzas as always:)