# On the Interaction of Representation Theory with Geometry and Combinatorics

Hausdorff Trimester Program

January - April 2011

**Organizers:** Steffen König, Peter Littelmann, Jan Schröer, Catharina Stroppel

Representation theory is one of the most vibrant fields of mathematics today. Starting with the pioneering work of Frobenius, Burnside and Schur, its history is a story rich in innovation and implementation of techniques from throughout mathematics. By its very nature, representation theory lies at the intersection of several fields: algebra, Lie theory, algebraic geometry, topology, number theory, differential geometry, combinatorics, harmonic analysis and mathematical physics.

**The Hausdorff Trimester** Program provided a forum and meeting place for exchange of ideas and techniques, focussing on topics connecting representation theory with different areas of mathematics. It brought together leading experts from representation theory, geometry, and combinatorics and, at the same time, enhanced the exchange between the various research networks.

The focus was on the following research topics:

- Geometrization, categorification and integral canonical structures
- Homological aspects of representation theory
- Representations of Cherednik algebras
- (Finite dimensional) algebras and cluster algebras
- Infinite-dimensional Lie algebras and related algebraic structures
- Combinatorics of flag varieties and Schubert calculus
- Hecke algebras, Koszul duality and tilting theory