Monday, July 8, 2013
Freie Universität Berlin
Institut für Informatik
Lecture - 14:15
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
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.