Graduiertenkolleg: Methods for Discrete Structures

Deutsche Forschungsgemeinschaft
faculty | junior-faculty | postdocs | students | associate students | former students | former associate students
|
locations | Term schedule | history
|
predoc-courses | schools | block-courses | workshops
partners


Monday Lecture and Colloquium


Monday, October 26, 2015

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



Lecture - 14:15

Tim Netzer - TU Dresden

Free Convexity

Abstract:
Instead of looking at convex sets in a real vectorspace only, free convexity deals with convex sets in all matrix algebras over the space simultaneously (or even involves operator algebras over the space). A suitable definition of convexity then connects the different levels, and gives rise to interesting phenomena and results. Considering such questions is well-motivated from such diverse areas as system- and control-theory, quantum physics and even PDEs. However, even simple operations as taking the convex hull are not completely understood. I will give an introduction to the topic, explain some important results, and also report on recent ongoing joint work with V. Alekseev and A. Thom.




Colloquium - 16:00

Alexander Engström - Aalto University

Graph colouring and the total Betti number

Abstract:
The total Betti number of the independence complex of a graph is an intriguing graph invariant. Kalai and Meshulam have raised the question on its relation to the cycles and the chromatic number of a graph, and a recent conjecture on that theme was proved by Bonamy, Charbit and Thomasse. We show an upper bound on the total Betti number in terms of the number of vertex disjoint cycles in a graph, and discuss it in the context of expanders.



Letzte Aktualisierung: 19.10.2015