I will attempt to keep the discussion as
self-contained as possible. This means I will NOT assume familiarity
with algebraic geometry, cohomology theories, characteristic
classes, etc. Rather than give a full exposition of all the
background needed (as this is impossible to do in one semester), I
will tell you enough about each topic so that you
can understand what is going on. I hope that what people see in the
course motivates them to learn more about each individual subject
(it worked for me!). In the first part of the course we will be
studying geometry, so it will help to have a general familiarity
with geometric reasoning.
For the most part we'll concentrate on the SL(n) case. The aim of the
course is to understand as much as we can about these examples;
even here there is current research with many unsolved problems.
There is room in the above description to cover some different topics
(for example, quantum cohomology or K-theory), depending on the
interests of the people attending.