Seventy-fourth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The 74th BLOC meeting will be held on Friday 1st July 2016 in the Department of Mathematics, University of Leicester. All lectures are in the George Porter Building, Lecture Room A (GP LTA). 


Programme:

Lunch: First floor, Charles Wilson Building (meet at front of College House at 12.30)

14.00 - 15.00 Niamh Farrell (City) The Morita Frobenius numbers of blocks of finite reductive groups

15.00 - 16.00 Amit Hazi (Cambridge) A linkage principle for the diagrammatic Hecke category

Tea

16.45 - 17.45 Jason Semeraro (Bristol) Saturated fusion systems over a Sylow p-subgroup of G2(p)

Please let Nicole Snashall know by June 23rd if you are coming to the BLOC meeting, and in particular if you wish to join us for lunch.


Abstracts

Niamh Farrell: The Morita Frobenius number of an algebra is the number of Morita equivalence classes of its Frobenius twists. In this project we aim to determine whether for blocks of quasi-simple finite groups there exists a bound on the Morita Frobenius number that depends only on the size of the defect group of the block. Here I present the latest results from this study and discuss their connections to Donovan’s Conjecture.

Amit Hazi: The diagrammatic Hecke category is an additive monoidal category over a field with a diagrammatic presentation. It provides a useful replacement for what is usually called the Hecke category (or the category of Soergel bimodules) over fields of positive characteristic. Determining the indecomposables in this category is a difficult problem, with connections to Kazhdan-Lusztig theory and modular representation theory of reductive algebraic groups. In this talk I will describe what I call a "linkage principle" for such categories over an affine Weyl group.

Jason Semeraro: This is joint work with Chris Parker.
A saturated fusion system $\F$ over a finite p-group S is a category whose objects are the subgroups of S, whose morphisms are monomorphisms between subgroups, and whose morphism sets satisfy certain axioms, formulated originally by Puig and motivated by properties of conjugacy relations between p-subgroups of a finite group.
Starting with a presentation for a Sylow p-subgroup S of G2(p) we determine which subgroups of S can control fusion in a saturated fusion system on S. Not surprisingly, this list includes the unipotent radicals of maximal parabolic subgroups of G2(p) but it turns out that there can be other possibilities. A key ingredient is the recently completed classification - due to Craven-Oliver-Semeraro - of indecomposable $\mathbb{F}_pG$-modules M where a cyclic Sylow p-subgroup of order p acts on M with exactly one non-trivial Jordan block. We obtain some new exotic fusion systems on S.


BLOC is supported by an LMS Scheme 3 grant, which is used to help offset travel costs for participants, with priority given to covering travel and accommodation costs for speakers and postgraduates.

Travel information is HERE.

There will be time for informal discussions during the meeting.


For further information please contact one of the organisers:

Joe Chuang
Karin Erdmann
Jeremy Rickard
Nicole Snashall

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University of Leicester
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Tel.: +44 (0)116 229 7407

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