Sixty-seventh BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The sixty-seventh meeting will be held on Wednesday 25th February 2015 in the Department of Mathematics, City University, London. All talks will take place in Room ELG11 in the Drysdale Building. Tea will be held in the Mathematics Common Room E215 in the Drysdale Building.


 

Programme:

12.15 Lunch: Banana Tree, 418 St. Johns Street

2.00 Sejong Park (Galway) Fusion systems and vanishing of derived limits

3.00 Ed Segal (Imperial) All autoequivalences are spherical twists

Tea

4.45 Jan Grabowski (Lancaster) Grading cluster algebras and categories

 


Abstracts

 

Sejong Park: Fusion systems are categories modeled on the p-fusion pattern of finite groups. Some fundamental questions about fusion systems can be formulated in terms of obstructions lying in derived limits of certain functors. I'm going to discuss recent progress in this type of problems involving the center functor and the cohomology functor. This is a joint work with Antonio Díaz.

Ed Segal: Seidel and Thomas found a symmetry of a triangulated category, called a spherical twist, using the idea of a 'spherical' object. Their construction was swiftly generalized to produce spherical twists around 'relatively-spherical' objects, and from there to a completely abstract construction of a twist around a 'spherical functor'. I’ll explain why this notion of a twist around a spherical functor is so general that any autoequivalence of a triangulated category can in fact be described as a spherical twist, for purely formal reasons.

Jan Grabowski: The idea of a graded cluster algebra has been around since the origin of the subject but often implicitly. However in the study of quantum cluster algebras, gradings play a much more prominent role, which prompts us to examine the classical case more carefully. We will transfer a definition of Gekhtman, Shapiro and Vainshtein into a more algebraic setting, to obtain the notion of a multi-graded cluster algebra. We then study gradings for finite type cluster algebras without coefficients and give a full classification. Translating the definition suitably again, we obtain a notion of multi-grading for (generalised) cluster categories. This setting allows us to prove additional properties of graded cluster algebras in a wider range of cases. We also obtain interesting combinatorics - namely tropical frieze patterns - on the Auslander-Reiten quivers of the categories.

 


 

 

Please let Joe Chuang know by February 20th 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. 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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