The 48th ARTIN meeting will take place at Newcastle University on the 1st and 2nd of September 2016. It will be funded by the London Mathematical Society and the Glasgow Mathematical Journal Trust.
We note that the preceding week in Belfast, there is a meeting of Algebra, Combinatorics, Dynamics, and Applications. The website can be found here: https://sites.google.com/site/algebrabelfast2010/acda2016.
-- Martin Herschend (Uppsala)
-- Gustavo Jasso (Bonn)
-- Robert Marsh (Leeds)
-- Kevin McGerty (Oxford)
-- Vanessa Miemietz (East Anglia)
-- Catharina Stroppel (Bonn)
Schedule of events:
Vanessa Miemietz (East Anglia) - Baby steps in p-dg 2-representation theory
1st September 2016, 2:00pm to 3:00pm -- Show/hide abstractAbstract: TBA
Martin Herschend (Uppsala) - Thick subcategories of n-cluster tilting subcategories
1st September 2016, 3:10pm to 4:10pm -- Show/hide abstractAbstract: In Iyama's higher dimensional Auslander-Reiten theory one shifts attention from module categories of algebras to so called n-cluster tilting subcategories for some fixed positive integer n. These are n-abelian (in the sense of Jasso) and so notions like kernel, cokernel and extension are replaced by their higher analogues: n-kernel, n-cokernel and n-extension, which are similar except that the exact sequences involved are longer. Thus it makes sense to consider subcategories of n-abelian categories that are closed under n-kernels, n-cokernels and n-extensions. We shall refer to these as thick subcategories. In my talk I will present a characterization of thick subcategories of n-cluster tilting subcategories with finitely many indecomposables. This will then be used to classify thick subcategories on n-cluster tilting subacategories for Nakayama algebras of global dimension n.
Catharina Stroppel (Bonn) - R-matrices and convolution algebras for Grassmannians
1st September 2016, 4:40pm to 5:40pm -- Show/hide abstractAbstract: In this talk I will describe in detail the combinatorics of equivariant cohomologies of Grassmannians, their Schubert classes (depending on a choice of Borel) and torus fixed point bases and connect them with the representation theory of Lie algebras. In particular we will construct R-matrices as a base change from one choice of Schubert class basis to another. In this way we will construct certain Bethe algebras which are important and interesting from the theory of integrable systems and Bethe bases. Finally we will connect this with the current algebra for sl_2 and the group algebra of the affine Weyl group and compare it briefly with constructions of Ginzburg, Maulik and Okounkov in a related but different setting.
Dinner at 'El Coto'
1st September 2016, 7:30pm to 9:30pm 21 Leazes Park Rd, Newcastle NE1 4PF
Gustavo Jasso (Bonn) - Mesh categories of type A-infinity and tubes in higher Auslander--Reiten theory
2nd September 2016, 9:15am to 10:15am -- Show/hide abstractAbstract: This is a report on ongoing work with Julian Kuelshammer. We construct higher analogues of mesh categories of type A-infinity and of the tubes from the viewpoint of Iyama's higher Auslander--Reiten theory. Our construction relies on unpublished work by Darpö and Iyama. We sketch a conjectural construction which relates our categories to spherical objects and to cluster tubes.
Kevin McGerty (Oxford) - Springer theory and symplectic resolutions
2nd September 2016, 10:30am to 11:30am -- Show/hide abstractAbstract: We will describe how an analogue of Springer's theory of Weyl group representations can be defined for a symplectic resolution of singularities, and explain what aspects of the classical theory survive in this more general set-up. For finite type Nakajima quiver varieties we will show how one recovers the Weyl group action of Lusztig, Nakajima and Maffei. This is joint work with T. Nevins.
Robert Marsh (Leeds) - Dimer models and cluster categories of Grassmannians
2nd September 2016, 12:00pm to 1:00pm -- Show/hide abstractAbstract: The homogeneous coordinate ring of the Grassmannian Gr(k,n) has a beautiful structure as a cluster algebra, by a result of J. Scott. Central to this description is a collection of clusters containing only Pluecker coordinates, which are described by certain diagrams in a disc, known as Postnikov diagrams or alternating strand diagrams. Recent work of B. Jensen, A. King and X. Su has shown that the Frobenius category of Cohen-Macaulay modules over a certain algebra, B, can be used to categorify this structure. In joint work with Karin Baur and Alastair King, we associate a dimer algebra A(D) to a Postnikov diagram D, by interpreting D as a dimer model with boundary. We show that A(D) is isomorphic to the endomorphism algebra of a corresponding Cohen-Macaulay cluster-tilting B-module, i.e. that it is a cluster-tilted algebra in this context. The proof uses the consistency of the dimer model in an essential way. It follows that B can be realised as an idempotent subalgebra of A.
Please register if you plan to attend, using the following link:
This will help us to organise refreshments, plan the conference dinner, and manage the budget.
The main workshop hotel is Osborne Hotel
which is about 20 minutes walk from campus. We have reserved 20 rooms B&B in the Osborne Hotel at the rate of £45 for one night on September 1 (some of the rooms may be in 'Dene Hotel' which is the sister hotel of the Osborne). We ask you to call the Osborne hotel yourself and to make a reservation, quoting 'Helen Green, School of Maths & Stats'. You will have to pay for this yourselves on the day, but postgraduate students and young researchers should apply for reimbursement upon registration. The Osborne Hotel holds the rooms until August 3rd, so please call them by that date, if you want to make use of the University rate.
The workshop dinner will take place at the Spanish restaurant El Coto (elcoto.co.uk). The meal will cost £15 per person (£10 for postgraduate students). Please make sure to register for the meeting if you plan to attend the meal.
The details will be updated on the ARTIN webpage
If you have any questions, please contact Stefan Kolb (firstname.lastname@example.org).
19:30- late: Dinner
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All talks will take place in Seminar Room 1.06 in Armstrong Building, which is number 22 on page 2 of the campus map
To find Room 1.06, enter Armstrong Building from the 'Old Quadrangle', and walk up the spiral stairs.