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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Classifying 2-blocks with an elementary abelian de
fect group - Cesare Giulio Ardito (University of M
anchester)
DTSTART;TZID=Europe/London:20200109T170000
DTEND;TZID=Europe/London:20200109T173000
UID:TALK136561AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/136561
DESCRIPTION:Donovan'\;s conjecture predicts that given a $p
$-group $D$ there are only finitely many Morita eq
uivalence classes of blocks of group algebras of f
inite groups with defect group $D$. While the conj
ecture is still open for a generic $p$-group $D$\,
it has been proven in 2014 by Eaton\, Kessar\, K&
uuml\;lshammer and Sambale when D is an elementary
abelian 2-group\, and in 2018 by Eaton\, Eisele a
nd Livesey when D is any abelian 2-group. The proo
f\, however\, does not describe these equivalence
classes explicitly. A classification up to Morita
equivalence over a complete discrete valuation rin
g $\\mathcal{O}$ has been achieved when $p=2$ for
abelian $D$ with rank $3$ or less\, and for $D=(C_
2)^4$.In my PhD thesis I have done $(C_2)^5$
\, and I have partial results on $(C_2)^6$. I will
introduce the topic\, give some definitions and t
hen describe the process of classifying these bloc
ks\, with a focus on the process and the tools nee
ded to produce a complete classification. All the
obtained data is available on https://wiki.manchester.ac.uk/blocks/
.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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