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Manchester Algebra Seminar - Cesare Giulio Ardito - Classification of blocks and open conjectures

Dates:1 December 2020
Times:13:00 - 14:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, Current University students
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  • Department of Mathematics

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  • In group "(Maths) Algebra"
  • In group "(Maths) Maths seminar series"
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Speaker: Cesare Giulio Ardito - City University of London

Title: Classification of blocks and open conjectures

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 many special cases. A harder question is the one to actually classify Morita equivalence classes in a given situation, i.e. to have a complete list of blocks that can occur determined up to Morita equivalence. In this talk, I will introduce the topic, give the relevant definitions and then roughly describe the process of classifying blocks, with a focus on the methodology and the tools normally needed to obtain such a result. Then I will focus on some applications of having such a list, mentioning some (perhaps surprising) difficulties that can arise in verifying certain classic modular representation theory conjectures, even when a complete list of blocks is given.

Title: TBC Time: 1pm

Place: Zoom

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Kieran Calvert

kieran.calvert@manchester.ac.uk

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