Wednesday, June 5, 17:00 and 18:30, room 306

Next Wednesday we have no talks, and this Wednesday we shall see two points of view towards the important phenomenon of hollow polytopes: lattice polytopes whose interior avoids the lattice.

17:00 Vjacheslav Zhukov: Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three We shall study lattice poyhedra whose interior avoids a given sublattice. The number of maximal (by inclusion) polyhedra of this type is finite modulo authomorphisms of the lattice. We shall prove this fact and see how to classify such polyhedra in dimension 3.

18:30 Evgeniy Pavlov: Hollow Convex Polytopes
This is the second talk in a series of lectures devoted to the study of convex bodies and polyhedra without interior lattice points. In this part we combine the results of Kannan, Lovasz and Pikhurko to show that every hollow lattice d-polytope either admits a projection onto a hollow lattice (d-1)-polytope, or belongs to one of finitely many exceptions.