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SUMMARY:Classifying 2-blocks with an elementary abelian defect group - Ces
 are Giulio Ardito (University of Manchester)
DTSTART:20200109T170000Z
DTEND:20200109T173000Z
UID:TALK136561@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Donovan&#39\;s conjecture predicts that given a $p$-group $D$ 
 there are only finitely many Morita equivalence classes of blocks of group
  algebras of finite groups with defect group $D$. While the conjecture is 
 still open for a generic $p$-group $D$\, it has been proven in 2014 by Eat
 on\, Kessar\, K&uuml\;lshammer and Sambale when D is an elementary abelian
  2-group\, and in 2018 by Eaton\, Eisele and Livesey when D is any abelian
  2-group. The proof\, however\, does not describe these equivalence classe
 s explicitly. A classification up to Morita equivalence over a complete di
 screte valuation ring $mathcal{O}$ has been achieved when $p=2$ for abelia
 n $D$ 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 then describe the process of classi
 fying these blocks\, with a focus on the process and the tools needed to p
 roduce a complete classification. All the obtained data is available on ht
 tps://wiki.manchester.ac.uk/blocks/.
LOCATION:Seminar Room 1\, Newton Institute
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