Lattice polytopes, recent results

Jean-Michel Kantor

Institut mathematique de Jussieu,Paris,France

April 29, ***Thursday at 2:30 ***

2-338

ABSTRACT 

The topic of lattice polytopes appears in many places in mathematics:

- geometry (geometry of polytopes ,algebraic geometry with toric varieties , singularity theory),

-computing (linear programming)

-number theory (diophantine linear equations),and others

We will consider some particular recent developments:

-counting lattice points in lattice polytopes:the Ehrhart polynomial, explicit formulas for its coefficients, complexity ,dependance on the lattice;

-Triangulations and classification of lattice polytopes with respect to locally unimodular mappings;

-Lattice-free (empty )polytopes, asymptotic estimation for the width ( with dimension going to infinity),number of equivalence unimodular classes of lattice-free polytopes.


Speaker's Contact Info: kantor(at-sign)math.mit.edu


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