Texas A&M University, Department of
Mathematics, 216 Milner Hall, 20th of April 2005, 3:00-3:50
Groups and Dynamics Seminar
MacKey functors:
from topology to algebraic geometry through group theory
Paulo Lima-Filho of Texas A&M
University
This talk will start with a quick overview of the notion of MacKey
functors, from their genesis in representation theory to their
appearance and important role in equivariant topology. Various examples
will be given, and amongst those we will focus on the Burnside ring for
finite groups. At this stage, algebraic geometry will make its
appearance and we will explain old results of A. Dress that describe
basic properties of the topology of the "spectrum of the Burnside ring"
(in the sense of Grothendieck). As a conclusion, one obtains an
interesting characterization of solvability in terms of this spectrum.
The aim of the talk is to present some problems to the audience, in an
attempt to generalize the results to the context of pro-finite groups
and virtual solvability.