Seventy-sixth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The seventy-sixth meeting will be held on Wednesday 8th March 2017 in the Department of Mathematics, City University, London. The talks are all in room ELG08, in the Drysdale Building (Northampton Square).


 

Programme:

12.15 Lunch: Banana Tree, 412-416 St. John Street, London EC1V 4NJ

13.45 Justin Lynd (Aberdeen) Automorphisms of fusion systems and linking systems

14.45 Peter Jørgensen (Newcastle) Thick subcategories of d-abelian categories

Tea

16.30 Rosie Laking (Bonn) Classification of indecomposable objects in the homotopy category of derived-discrete algebras

 


 

Abstracts

Justin Lynd: There has been interest recently in comparing the outer automorphism groups of finite simple groups with the outer automorphism groups of their linking and fusion systems at a fixed prime p. In particular, Andersen-Oliver-Ventura, Broto-Moller-Oliver, and Oliver have now made this comparison for all finite simple groups and at all primes p. I will discuss how a piece of this work allows one to describe the outer automorphism groups and almost simple extensions of the exotic Benson-Solomon systems at the prime 2 (joint with E. Henke). I'll also discuss a general result (joint with G. Glauberman), that restricts the structure of the kernel of the map from the outer automorphism group of a linking system to that of the fusion system.

Peter Jørgensen: Report on joint work with Martin Herschend and Laertis Vaso.
Let d be a positive integer.  The notion of d-abelian categories was introduced by Jasso.  Such a category does not have kernels and cokernels, but rather d-kernels and d-cokernels which are longer complexes with weaker universal properties.  Canonical examples of d-abelian categories are d-cluster tilting subcategories of abelian categories.
We introduce the notion of thick subcategories of d-abelian categories.  We show that functorially finite thick subcategories of d-cluster tilting subcategories are in bijection to so-called d-rigid epimorphisms.  This generalises a classic result by Geigle and Lenzing.
We apply this to show a classification of the thick subcategories of a family of d-abelian categories associated to quivers of type An.

Rosie Laking: An algebra A is said to be derived-discrete if there are only finitely many indecomposable complexes in the bounded derived category of A with any given homology dimension vector.  One very well-known family of derived-discrete algebras are those that arise as path algebras of ADE-Dynkin type quivers.  Vossieck was able to show that the only other derived-discrete algebras are gentle and moreover representatives of these remaining derived equivalence classes were later classified by Bobinski, Geiss and Skowronski.
In this talk I will present joint work with K. Arnesen, D. Pauksztello and M. Prest, in which we study categories of functors from the bounded derived category of a derived-discrete algebra to the category of abelian groups.  The bounded derived category is equivalent to the full subcategory of compact generators of the homotopy category K(ProjA) of projectives over A.  Using methods arising from the model theory of modules, we are able to classify the indecomposable objects in this category and show that they are all pure-injective and have finite endolength.

 


 

Please let Jorge Vitória know by March 3rd if you are coming to the meeting, especially if you are coming for lunch and/or wish to stay for a meal in the evening.

 

There will be time for informal discussions during the day.

The meeting is supported by an LMS Scheme 3 grant. This is used to help offset travel costs for those from institutions participating in the scheme, with priority given to speakers and postgraduates. The funds available in 2016/17 are limited, so if you require funding then please let Jorge know in advance. Please note that, if travelling by train, then you should purchase an advance ticket where possible, since the grant will not cover standard open return tickets to London during peak hours.

Travel information is HERE.


For further information please contact one of the organisers:

Joe Chuang
Karin Erdmann
Jeremy Rickard
Nicole Snashall

 

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