Wednesday, April 3, 18:30, room 306

Dmitry Leonkin

Finitely many lattice polytopes of a given volume

In our quest for classification of small lattice polytopes it’s absolutely crucial to prove finiteness of equivalency classes of polytopes with fixed volume (or with fixed positive number of interior points). We will prove that every lattice polytope in R^n of volume <= V is integrally equivalent to a lattice polytope, contained in lattice cube of side length at most n*n!*V. To deduce the result about polytopes with fixed number of interior points we will investigate boundaries for volume of polytope with given amount of interior lattice points. The talk is based on papers by Lagarias, Ziegler and Hensley.