SMS scnews item created by Alex Sherman at Mon 16 Oct 2023 1028
Type: Seminar
Modified: Mon 16 Oct 2023 1217
Distribution: World
Expiry: 15 Jan 2024
Calendar1: 20 Oct 2023 1200-1300
CalLoc1: Carslaw 173
CalTitle1: Algebra Seminar: TBA
Auth: (ashe8718) in SMS-SAML

Algebra Seminar: Treumann -- G-spectra of cyclic defect

David Treumann (Boston College) is speaking in the Algebra Seminar this week.  We will
go out for lunch after the talk.  

When: Friday, 20 October, 12-1pm 

Where: Carslaw 173 

Title: G-spectra of cyclic defect 

Abstract: The talk is titled after a paper I wrote with Tony Feng and Allen Yuan.  "G"
stands for a finite group, "G-spectra" are objects of algebraic topology that resemble
representations of a finite group, especially modular representations.  "Defects" are
invariants of "blocks," not featured in the title but a main subject of the talk.
Mainly I will use the talk as an excuse to give an introduction to "Broue’s Abelian
Defect Conjecture." 

Broue’s conjecture predicts that a block of Z_p[G] and of Z_p[N] (group rings) have
equivalent derived categories, when N is the normalizer of the defect group of the block
and this defect group is commutative.  In case the defect group is cyclic, there are two
old proofs of it, one by Rickard and a while later one by Rouquier.  Feng and Yuan and I
can construct a similar equivalence between blocks of p-complete G-spectra and
p-complete N-spectra, that induces Rouquier’s equivalence after taking homology.

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