March 6, Wednesday, 18:30, room 306

Fedor Selyanin

LATTICE VERTEX POLYTOPES WITH INTERIOR LATTICE POINTS

Consider a convex polytope with lattice vertices and at least one interior lattice point. We will prove that the number of boundary lattice points is bounded from above by a function of the dimension and the number of interior lattice points. We will find the boundaries for zero symmetric convex polytopes, then for arbitrary lattice polytopes and compare them.
This is the starting point to many results on classification of small lattice polytopes that will be presented in subsequent talks.