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:
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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 Laplace-type 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), 49-149. |
2. | A. Bernstein and A.V. Zelevinsky: Total positivity in Schubert varieties. Comm. Math. Helv. 72 (1997), 128-166. |
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 |