Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium


Monday, January 18, 2016

TU Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041



Lecture - 14:15

Jens Marklof (FRS) - University of Bristol


Emerging applications of homogeneous flows: From discrete mathematics to statistical physics

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

Sören Berg - TU Berlin


Lattice points in centered convex bodies

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.




Letzte Aktualisierung: 08.01.2016