Information on the main courses 
(7 hours each) 
Information on the main courses has been provided by the the lecturers and can be found below.
There is also information available on
J.J. Duistermaat:  Lefschetz fixed point fomulas for equivariant differential operators 
The course will be based on the book:
The students are encouraged to obtain this book in advance and to bring it to the lectures. A few extra copies will be available for reference during the course.
Prerequisites:
1.  Absolutely necessary preliminary knowledge: 
Differential geometry, including manifolds, vector bundles, connections, differential forms, actions of Lie groups.  
Literature:


2.  Relevant preliminary knowledge: 
a. Linear operators of trace class in a Hilbert space.  
The book of Dunford and Schwartz is a bible for this. A simpler textbook on Hilbert space might be preferred if it treats operators of trace class.  
b. Linear partial differential operators.  
In particular Laplacetype operators for Riemannian manifolds.  
c. De Rham Cohomology.  
The books on differential geometry should also provide sufficient background for b. and c. 
M. Yoshida:  Hypergeometric Functions 
The course will be based on the book:
The students are encouraged to obtain this book in advance and to bring it to the lectures. A few extra copies will be available for reference during the course.
Prerequisites:
No special prerequisites, only the basics of mathematics.
A.V. Zelevinsky:  Total positivity and double Bruhat decomposition 
The lecture will be based on the two papers:
1.  A. Bernstein, S. Fomin and A.V. Zelevinsky: Parametrizations of canonical bases and totally positive matrices. Adv. in Math. 122 (1996), 49149. 
2.  A. Bernstein and A.V. Zelevinsky: Total positivity in Schubert varieties. Comm. Math. Helv. 72 (1997), 128166. 
Prerequisites:
Standard knowledge of basic Lie theory and some facts about semisimple Lie algebras.
R.J.Stanton:  Geometric analysis on locally symmetric spaces 
I.B. Frenkel:  Representation Theory and Quantum Field Theory 
S.C. Hille; tel. +31 71 5277109; Revised: 27 May 1997 