#
Monday Lecture and Colloquium

**Monday, December 10, 2007 **

Freie Universität Berlin

Institut für Informatik

Takustr. 9,

room 005

** Lecture - 14:15**

###
Martin Aigner - FU Berlin

### A proof that is not yet in the Book

*Abstract:*

**Colloquium - 16:00**

###
Benjamin Nill - FU Berlin

###
The degree of lattice polytopes

*Abstract:*

Given a lattice polytope P, let G(n) be the number of lattice points in
the n-th dilate of P. This function is a polynomial, called Ehrhart
polynomial of P. Moreover, the generating function of the sequence of
numbers G(n) is a rational function whose numerator is a polynomial with
non-negative integers, which we call the h*-polynomial of P.
These fundamental results are due to Ehrhart and Stanley.
In this talk we deal with the degree of the h*-polynomial
which we also call the degree of P. This invariant equals at most the
dimension of the polytope, with equality if and only if P contains
an interior lattice point.
We propose that the degree may be regarded as a kind of
"lattice dimension" of a lattice polytope.
As evidence in favour of this interpretation we
present recent results and ongoing work
on a conjecture of Batyrev, with an elementary proof in the case of a
lattice simplex.

Letzte Aktualisierung:
27.11.2007