Monday, January 18, 2016
TU Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041
Lecture - 14:15
Abstract:
The theory of homogeneous flows provides a powerful mathematical toolkit that has recently contributed to the solution of a number of longstanding problems. I will survey some of the recent progress, including a study of distances in multi-loop networks (circulant graphs), the coin exchange problem and the derivation of a new kinetic equation which captures surprising transport phenomena in crystals and quasicrystals. This lecture is aimed at a broad audience.
Colloquium - 16:00
Abstract:
A convex body K is said to be symmetric if K=-K. A well-known theorem by
Hermann Minkowski states that if a convex body K is symmetric and contains
no point of the integer lattice in its interior except for the origin,
then the number of integral lattice points overall in K is bounded above
by 3^d. In this talk we will discuss a generalization of this theorem by
considering convex bodies which are not necessarily symmetric yet having
their centroid at the origin. For simplices we will present a best
possible bound in particular. A relation to a well-known conjecture by
Ehrhart will also be covered briefly.
This is joint work with Martin Henk.