### Friday September 29, 2006, 11 AM **(Note
new time!)**, Goldsmith 226

**Speaker**: George McNinch (Tufts)

**Title**: Nilpotent orbits of a reductive group in positive
characteristic

**Abstract**: Let *K* be a field and let *G* be a reductive
group over *K*. Examples
include the general linear group of a (finite dimensional) *K*-vector
space, the group of units of a central simple *K*-algebra, orthogonal
and symplectic groups, as well as some "exceptional groups". In the
study of the structure and representations of *G*, one is often
interested in conjugacy classes. The Jordan decomposition essentially
reduces one to a study of semisimple classes and of unipotent
classes. The "discrete part" of this study is the unipotent variety -
there are only finitely many "geometric" unipotent classes. Under mild
assumptions on the characteristic, the unipotent classes may be
identified with the nilpotent variety in Lie(*G*), permitting one
to "linearize" the problem somewhat. The talk will discuss the
Bala-Carter theorem classifying the geometric nilpotent oribts in
"good" characteristic; we will mention Premet's recent proof of that
theorem.

We then explain how Galois cohomology of the centralizer
*C*_{G}(*X*) of a *K*-rational nilpotent element
*X* permits one to ponder the orbits of the group of rational points
*G*(*K*) on the nilpotent elements of Lie(*G*)(*K*).
This motivates interest in the structure of such a centralizer; we will
then describe various results about *C*_{G}(*X*) (which
are mainly interesting when the field *K* has positive
characteristic).