Sixty-ninth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The 69th BLOC meeting will be held on Monday 29th June 2015 in the Department of Mathematics, University of Leicester. All talks will be in George Porter Building Lecture Room A (GP LTA).


 

Programme:

Lunch: First floor, Charles Wilson Building (meet at front of College House at 12.00)

13.30 - 14.30 Rachel Taillefer (Clermont-Ferrand) On a generalisation of N-Koszul algebras for Brauer graph algebras
(Abstract below)

14.30 - 15.30 Ha Thu Nguyen (Cambridge) First cohomology groups and a conjecture of Hemmer

Tea

16.15 - 17.15 Mark Wildon (Royal Holloway) Bell numbers, box moves and the eigenvalues of the random-to-top shuffle
(Abstract below)

Dinner

 

Please let Sibylle Schroll or Nicole Snashall know by June 19th if you are coming to the BLOC meeting, and in particular if you wish to join us for lunch or stay for a meal in the evening.


Abstracts:

Rachel Taillefer On a generalisation of N-Koszul algebras for Brauer graph algebras
Koszul algebras are a well-known and much studied class of algebras. These were generalised in 2001 by Roland Berger to N-Koszul algebras. This means that if we write the algebra as a quotient of a tensor algebra A=Tk(V)/I, the ideal I can be generated by elements of degree N and that the projective modules in a minimal graded projective resolution of k can be generated in specific degrees depending on N. Moreover, the Ext algebra of k is generated in degrees 0, 1 and 2. This notion has been generalised since in several ways. We are interested in two of them: - an algebra is called K2 if it is graded and if its Ext algebra is generated in degrees 0, 1 and 2 [Cassidy-Shelton]; - an algebra A=Tk(V)/I is called 2-d-determined if the ideal I can be generated by elements of degrees 2 and d, where d>2 is an integer, and the projective modules in a minimal graded projective resolution of k can be generated in specific degrees depending on 2 and d [Green-Marcos]. The aim of this talk is to give examples of such algebras, within the class of Brauer graph algebras, and to compare K2 Brauer graph algebras and 2-d-determined Brauer graph algebras. This is joint work with E.L. Green, S. Schroll and N. Snashall.

Mark Wildon Bell numbers, box moves and the eigenvalues of the random-to-top shuffle
Let Bt(n) be the number of partitions of a set of size t into at most n subsets. If n is at least t then Bt(n) is the classical Bell number Bt. In my talk I will describe two new combinatorial interpretations of the numbers Bt(n), using sequences of box moves on Young diagrams and sequences of random-to-top shuffles. I will then introduce Solomon's Descent Algebra and use it to sketch the proofs. A corollary is a very short proof of a result, originally due to Diaconis, Fill and Pitman, on the eigenvalues of the k-random-to-top shuffle. If time permits I will discuss the analogous results for the Coxeter group of Type B. This talk is on joint work with John R. Britnell (Imperial College).


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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Department of Mathematics
University of Leicester
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Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 229 7407

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