Manchester Algebra Seminar - Cesare Giulio Ardito -Donovan’s conjecture and the classification of blocks
|Starts:||14:00 25 Feb 2020|
|Ends:||15:00 25 Feb 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Cesare Giulio Ardito (University of Manchester)
Title: Donovan’s conjecture and the classification of blocks
Abstract: Donovan’s conjecture predicts that given a p-group D there are only finitely many Morita equivalence classes of blocks of group algebras with defect group D. While the conjecture is still open for a generic p-group D, it has been proven in 2014 by Eaton, Kessar, Kuelshammer and Sambale when D is an elementary abelian 2-group, and in 2018 by Eaton and Livesey when D is any abelian 2-group. The proof, however, does not describe these equivalence classes explicitly.
A classification up to Morita equivalence over a complete discrete valuation ring O has been achieved for D with rank 3 or less, and for D = (C_2)^4 . I have done (C_2)^5 , and I have partial results on (C_2)^6 . In this talk I will introduce the topic, give the relevant definitions and then describe the process of classifying these blocks, with a particular focus on the methodology and the individual tools needed to achieve a complete classification.
There will be tea and biscuits at 1:45. All are welcome.
Travel and Contact Information
Frank Adams 1 (FA1)
Alan Turing Building