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.