**BILKENT
ALGEBRA / TOPOLOGY SEMINAR**

**"How Phases Appear When Reducing to
Quotient Groups, for Instance, as in Alperin's Conjecture"**

By

# LAURENCE BARKER

# (Bilkent University)

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**Abstract:** This talk is a pedagogical introduction.Clifford
theory reduces to quotient groups, but with the introduction of a twist: a
phase factor, a cohomology class. Alperin's
Conjecture says that the number of simples of a block is "locally determined"
in terms of subquotients N(P)/P
for p-subgroups P. After Puig, "locally
determined" means determined by the fusion system up to finite information.
But the fusion system, a category consisting of conjugation homomorphisms
between p-subgroups, cannot see the subquotients PC(P)/P. To express Alperin's
Conjecture in a truly local way, Clifford theory is applied to quotient out PC(P)/P from N(P,e)/P, where e is
a suitable block of PC(P). The extra information in the introduced twists is
finite.

**Date: ****Monday, November 18, 2013**

**Time: ****13.40-14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

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**All are most cordially invited.**

Tea and cookies will be served after the talk.