Sixty-eighth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The 68th BLOC meeting and Representation Theory workshop forms part of the joint BMC/ BAMC which will be held at The University of Cambridge from Monday 30 March to Thursday 2 April 2015.

 

Please note that participants MUST register for the BMC. The BMC webpage is here. The deadline for early bird registration is 7 February 2015, after which date the registration fee will increase from £115 to £150.

 

 

The Representation Theory workshop takes place in the afternoons of Monday 30 March and Wednesday 1 April.

 

 


 

 

Monday 30 March

 

2.00 Neil Saunders (Bristol) Exotic Springer Fibres

3.00 Ilke Canakci (Leicester) Ptolemy relations in terms of modules over (gentle) Jacobian algebras

 

Wednesday 1 April

 

2.00 Melanie de Boeck (Kent) Foulkes modules for the symmetric group

3.00 Chris Bowman (City University) On graded decomposition numbers of rational Cherednik algebras

 


 

Abstracts

Neil Saunders: Exotic Springer Fibres
Abstract: Let G be a connected reductive algebraic group over the complex numbers, say, and let W be its Weyl group. The Springer Correspondence is a bijection between G-equivariant local systems on the G-orbit closures on the nilpotent cone of its Lie algebra, and certain irreducible representations of the Weyl group. Explicitly, the representations come from W-actions on the cohomology of the so-called Springer fibres. This is somewhat mysterious as W does not act on every Springer fibre, but does act on the cohomology of every Springer Fibre.

Generally, Springer fibres are difficult to describe geometrically; however their irreducible components often admit nice combinatorial descriptions. In this talk I will give a general exposition on the Springer Correspondence and report on work in progress that seeks to describe the irreducible components of the exotic Springer Fibres in type C. This is joint work with Vinoth Nandakumar.

Ilke Canakci Ptolemy relations in terms of modules over (gentle) Jacobian algebras
Abstract: The well-known Ptolemy relations relate the four sides and two diagonals of a quadrilateral. In joint work with S. Schroll, we show that these relations give rise to short exact sequences between indecomposable modules over (gentle) Jacobian algebras and use this result to address a longstanding problem for a class of gentle algebras, namely constructing a basis for the extension space between indecomposable modules. Our approach is new and uses cluster algebras and cluster categories associated to marked surfaces as well as so-called snake graph combinatorics. This talk does not require any background on cluster algebras.

Melanie de Boeck: Foulkes modules for the symmetric group
Abstract: The action of the symmetric group Smn on set partitions of sets of size mn into n sets of size m gives rise to a permutation module called the Foulkes module. Structurally, very little is known about Foulkes modules, even over C. In this talk, we will introduce Foulkes modules and their twisted analogues before presenting some results which shed light on the irreducible constituents of the ordinary characters of twisted Foulkes modules. Time permitting, we will discuss the modular structure of a certain twisted Foulkes module.

Chris Bowman: On graded decomposition numbers of rational Cherednik algebras
Abstract: We shall give an algorithmic description of a family of graded decomposition numbers for Cherednik algebras with a FLOTW weighting. This is joint work with Anton Cox and Liron Speyer.

 

 


 

The BMC webpage with links to the programme and registration/ accommodation costs is here.

The organisers of this BLOC meeting/Representation Theory workshop are Stuart Martin and Nicole Snashall.

 

 

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. Funds are limited so if participants can find funding from other sources that is helpful!

There are details of additional funds for student support available on the BMC registration page; please note that the deadline for applying for these funds is 11 January 2015. For more information about funding from BLOC for this meeting, please email Nicole Snashall.

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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