## Oberwolfach-Seminar: Representation Theory and Applications

Date:
November 19th - November 25th, 2006
Organizers:
Peter Littelmann, Köln
Nicolai Reshetikhin, Berkeley
Programme:
The most significant results in mathematics are obtained when combining methods and ideas from different fields of mathematics and different scientific schools. Representation theory has always been an important tool in many areas of mathematics and theoretical physics. Naturally, questions motivated by applications have strongly influenced research in representation theory In this Oberwolfach seminar we are going to work out three aspects of this mutual influence.

The first course focuses on algebraic-geometric aspects of representation theory. Kari Vilonen (Chicago) will give in his lectures an introduction into the geometric Langlands program and also report on latest developments.

The second course will be held by Nicolai Reshetikhin (Berkeley). He will focus on aspects of statistical mechanics related to the representation theory of $gl_\infty$, to statistics of various plane partitions.

Some recent developments in representation theory motivated by theoretical physics will be represented in Tetsuji Miwa’s course (Kyoto) on the construction of monomial basis of representations of vertex operator algebras. The key words here are Bosonic vertex operators, the affine $sl_2$-Kac-Moody algebra and Virasoro minimal series.

Prerequisites:
A necessary background for the seminar is the knowledge of representation theory of semisimple Lie algebras or semisimple algebraic groups, or compact groups. Some basic knowledge on the theory of affine Kac-Moody groups and/or algebras is recommended.
Literature:
• (will be announced soon)
October 1, 2006

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.

Mathematisches Forschungsinstitut Oberwolfach   updated: January 23rd, 2006