#
Monday Lecture and Colloquium

**Monday, July 8, 2013**

Freie Universität Berlin

Institut für Informatik

Takustr. 9

14195 Berlin

room 005

** Lecture - 14:15**

### Volkmar Welker -
Philipps-Universität Marburg

###
Polytopal, combinatorial and algebraic aspects of statistical ranking models

*Abstract:*

This talk describes and studies some of the standard statistical ranking models. Here we see a
ranking as a permutation of n objects and a ranking model then is a probability distribution
on the symmetric group. In this talk we are interested in ranking models for which the
probability distribution on the symmetric group for each permutation is a rational function
in a set of parameters. I will explain some combinatorial, polytopal and algebraic
aspects of this type of ranking models.

** Colloquium - 16:00**

### Jean-Philippe Labbé -
Freie Universität Berlin

### Higher-Dimensional Kaleidoscopes

*Abstract:*

Imagine yourself sitting on a vertex of a polytope P in Euclidean space R^d, where mirrors are placed at the perpendicular bisector of each edge of P.

When you look around, how many copies of yourself do you see?

In this talk, we will describe a characterization of polytopes P giving finitely many mirror-images, which is the object of Gelfand--Serganova's Theorem. This result calls for a generalization of the concept of matroid called Coxeter matroid. Besides this characterization of higher-dimensional kaleidoscopes, we will demonstrate how Coxeter matroids can be used to shed some light on the relation between the symmetric group and usual matroids.

Letzte Aktualisierung:
19.06.2013