Colloquium of Labex Bezout May 19, 2015

In Auditorium Maurice Gross - Bâtiment Copernic UPEM

Program of the colloquium

  9h30 - 10h00 :  Welcoming participants

10h00 - 11h00 : Mikhail Berlinkov (Ekaterinburg Russia)

                        "Synchronizing automata and the Cerny conjecture"

11h00 - 11h30 : Coffee break

11h30 - 12h30 : Imre Barany (Budapest and London)

                        "Extremal problems for convex lattice polytopes" 

In this survey I will present several extremal problems, and some solutions, concerning convex lattice polytopes. A typical example is to determine the minimal volume that a convex lattice polytope can have if it has exactly n vertices. Other examples are the minimal surface area, or the minimal lattice width in the same class of polytopes. These problems are related to a question of V I Arnold from 1980 asking for the number of (equivalence classes of) lattice polytopes of volume V in d-dimensional space, where two convex lattice polytopes are equivalent if one can be carried to the other by a lattice preserving affine transformation.