Lattice polytopes, recent resultsJeanMichel KantorInstitut mathematique de Jussieu,Paris,France
April 29, ***Thursday at 2:30 ***

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; Latticefree (empty )polytopes, asymptotic estimation for the width ( with dimension going to infinity),number of equivalence unimodular classes of latticefree polytopes. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

