**Department of Mathematics**

**COLLOQUIUM**

"Local structure of groups and of their classifying spaces"

BOB OLIVER

`(Université Paris 13)`

ABSTRACT: The fusion system of a finite group *G* at a prime p is a category whose objects
are the subgroups of a fixed Sylow p-subgroup *S*≤*G*, and whose morphisms are those homomorphisms between
subgroups which are induced by conjugation in *G*. It
thus encodes the conjugacyrelations among p-subgroups and elements of p-power order in *G**.* Fusion systems
have emerged as tools for studying the local structure of finite groups at a
given prime, and also the local structure of their classifying spaces. For
example, some group theorists hope that this new point of view will help to
simplify some parts of the proof of the classification of finite simple groups.
This will be a survey talk, aiming to explain both of these connections.

**Wednesday, MAY 4, 2016**** ****15.40**

**Mathematics Seminar Room,
SA-141**

**All are most cordially invited. Tea
and cookies: before the seminar**