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.

[Duistermaat | Frenkel | Stanton | Yoshida | Zelevinsky ]

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:
  • Spivak: Differential Geometry, or
  • Helgason: Differential Geometry and Symmetric Spaces, or
  • Kobayashi and Nomizu,
or any other good textbook on differential geometry.
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.
and on a paper in preparation by S. Fomin and A.V. Zelevinsky. The organizers will provide (a selection of) off-prints. A preprint can also be obtained from the web.

Prerequisites:

Standard knowledge of basic Lie theory and some facts about semisimple Lie algebras.


R.J.Stanton: Geometric analysis on locally symmetric spaces
A set of lecture notes will be available during the course.
I.B. Frenkel: Representation Theory and Quantum Field Theory

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S.C. Hille; tel. +31 71 5277109;
Revised: 27 May 1997