About The Workshop





How to reach ISI


The theory of algebraic groups is a beautiful and complete theory. Other than being intrinsically interesting, it is also central to many areas of mathematics like Representation theory, Number theory, Geometry and Topology, Harmonic Analysis etc. To give an example, the Langlands program, a grand unifying principle in modern day mathematics which brings many of the above subjects together, needs the theory of algebraic groups to even state the basic theorems and conjectures.

This workshop is a continuation of the instructional workshop ``Classification of Reductive Algebraic Groups" held at the Indian Statistical Institute, Bangalore Centre, during 18th December 2006 - 5th January 2007, in which the classification of reductive algebraic groups over an algebraically closed field, were discussed (roughly the contents of Chapter 1 to 10 of [2] below).

In this workshop, we plan to discuss rationality questions and given an introduction to the theory of modular representations of reductive algebraic groups over a field of prime characteristic.

Each day of the workshop will have four lecture hours and one hour devoted to examples and exercises.

A potential participant would be a Ph.D. student, or a very advanced M.Sc. student, or a mathematician wanting to learn this subject. The prerequisites for the workshop are:
  • A thorough knowledge of linear algebra and familiarity with some multilinear algebra.
  • Some elementary algebraic geometry.
  • Familiarity with `structure theory and representation theory of Complex semisimple Lie algebras'.

It would be very helpful to be familiar with atleast a clear and complete statement of the classification of reductive algebraic groups over an algebraically closed field.

We will post some notes on these prerequisites for the workshop by the 3rd March 2008. Selected participants are urged to study these notes before the workshop.

The reference material for the workshop are:
  1. Introduction to Lie algebras and representation theory, 
  2. By James Humphreys,
    Graduate Texts in Mathematics, 9. Springer-Verlag,
    New York-Berlin, 1978. ISBN 0-387-90053-5.
  3. Linear algebraic groups.
  4. By T.A. Springer,
    Second edition. Progress in Mathematics 9, Birkhauser Boston, Inc., Boston, MA, 1998. ISBN 0-8176-4021-5.
  5. Representations of Algebraic groups.
  6. By R. Steinberg,
    Nagoya Math. J. 22 (1963) 33-56.
  7. Endomorphisms of Linear Algebraic Groups.
  8. By R. Steinberg,
    Memoirs AMS (1968).
Subject to budget approval, local hospitality will be provided to all participants and travel support will be available to selected participants.

Deadline for application:- 1st February 2008.
For further information, please contact:-
N.S.N. Sastry (nsastry@isibang.ac.in)

This page was last modified on October 4, 2007.

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