250096 VO Selected topics in combinatorics (2009W)

This will be a course on the combinatorics of reflection groups. A reflection
group is a group which is generated by reflections in an Euclidian space R^d. The simplest examples are the dihedral groups (the symmetry groups of regular n-gons) and the symmetric group S_n. In the past few years, authors such as Armstrong, Athanasiadis, Bessis, Brady, Chapoton, Fomin, Reading, Reiner, Watt, Zelevinsky (and also the lecturer) have laid out a colourful spectrum of various combinatorial objects that are associated to reflection groups, and which run under imaginative names such as "associahedron", "cluster complex", "non-crossing partitions", "nnon-nesting partitions", or "Shi arrangement." These objects possess various beautiful properties (where, partially, the explanations are missing until today) concerning enumeration and structural properties. Since these objects are at the crossroads of several mathematical theories, working with these objects will give us the opportunity to penetrate the theory of reflection groups, the theory of polytopes, the theory of hyperplane arrangements, the enumeration of maps, multivariate Lagrange inversion, among others. It is not a prerequisite to already have attended a course on reflection groups.

Due to a research stay abroad of the lecturer, this course will be held
from November 3 until end of January.