Title: Character theory of finite groups

Lecturer: 
I Martin Issacs 
University of Wisconsin (Madison) 

Abstract: 
Characters provide a comparatively easy way to work with complex 
representations of finite groups, and they are a powerful
tool for proving theorems about such groups.

Early in the 20th century, for example, Burnside and
Frobenius used characters to prove theorems that were otherwise
inaccessible. (The theorem of Burnside, but not that of Frobenius,
can now be proved without characters.) 

The use of characters to prove group-theory theorems
continued well into the second half of the 20th century, but that
is no longer the focus of research; characters have become objects
of study in their own right.

Surprising connections between the characters of a group
and of certain of its subgroups were observed, and these have led
to a number of striking conjectures, many of which are still open.

The individual lecture titles are:

(1) Introduction to character theory.
(2) Burnside's theorem on groups of order p^a q^b.
(3) Frobenius' theorem on permutation groups where
    nonidentity elements fix at most one point.
(4) Conjectures and recent developments.