The 46th ARTIN meeting will take place at the University of Glasgow on the 6th and 7th of November 2015. More details will appear here soon.
Speakers:
 Giovanni Cerulli Irelli (Rome)
 Xin Fang (Cologne)
 Martina Lanini (Edinburgh)
 Markus Reineke (Wuppertal)
 Johan Martens (Edinburgh)
 Ben Martins (Aberdeen)
Tentative Schedule:

ARTIN 46
23rd November 2017, 8:18pm to 8:18pm 
Martina Lanini (Edinburgh)  Degenerate flags and Schubert varieties
6th November 2015, 2:00pm to 3:00pm  Show/hide abstractAbstract: Introduced in 2010 by Evgeny Feigin, degenerate flag varieties are degenerations of flag manifolds, naturally arising from a representation theoretic context. In this talk, I will discuss joint work with G. Cerulli Irelli, and G. Cerulli Irelli and P. Littelmann, in which we show that such degenerations in type A and C not only share a lot of properties with Schubert varieties (as previously proven by Feigin, Finkelberg and Littelmann), but are in fact Schubert varieties in an appropriate flag manifold. 
Johan Martens (Edinburgh)  GelfandCetlin revisited
6th November 2015, 3:00pm to 4:00pm  Show/hide abstractAbstract: In 1950 Gel'fand and Cetlin constructed the first example of what we now call canonical bases for the representations of a semisimple Lie algebra. Much later Guillemin and Sternberg showed how these could be understood as arising out of the geometric quantization of flag varieties or coadjoint orbits in various polarisations, relying on a (real) integrable system that is closely related to toric degenerations of these flag varieties. We shall outline this story, and then indicate how this symplectic story generalises using contractions of Hamiltonian spaces. This is based joint work with Joachim Hilgert and Chis Manon. 
Coffee Break
6th November 2015, 4:00pm to 5:00pm 
Giovanni Cerulli Irelli (Bonn)  Quiver Grassmannians associated with Dynkin quivers
6th November 2015, 5:00pm to 6:00pm  Show/hide abstractAbstract: Given a quiver Q and a finite dimensional Qrepresentation M, a quiver Grassmannian associated with M parametrizes the subrepresentations of M of a fixed dimension vector. Such projective varieties appeared in the work of Schofield, for the study of general properties of Qrepresentations. More recently, it was discovered that their Euler characteristic plays a prominent role to categorify cluster algebras associated with Q. It is natural to ask about their geometric properties but it turns out that their geometry can be arbitrarily complicated. In this talk I will restrict my attention to the case when Q is an orientation of a simplylaced Dynkin diagram: In a series of papers with Markus Reineke and Evgeny Feigin, we have developed tools in order to study the geometry of such varieties. Such tools are useful to study classes of quiver Grassmannians of Dynkin type. For example, and this was our motivation, degenerate flag varieties of type A can be realized as a "wellbehaved" quiver Grassmannian of Dynkin type. I will overview this tools and provide several applications. 
Dinner: TBA
6th November 2015, 7:00pm to 8:00pm 
Ben Martin (Aberdeen)  Complete reducibility for reductive algebraic groups.
7th November 2015, 10:00am to 11:00am  Show/hide abstractAbstract: Let G be a reductive algebraic group over a field k of positive characteristic. The notion of a completely reducible subgroup of G generalises the notion of a completely reducible representation (which is the special case when G=GL_n(k)). I will describe a geometric approach to the theory of complete reducibility, based on ideas of R.W. Richardson, and I will discuss some recent work involving nonalgebraically closed fields. 
Coffee Break
7th November 2015, 11:00am to 12:00pm 
Xin Fang (Köln)  New filtrations and monomial bases of quantum groups
7th November 2015, 12:00pm to 1:00pm  Show/hide abstractAbstract: For a Lie algebra of type A or C, E. Feigin, G. Fourier and P. Littelmann constructed a monomial basis for any finite dimensional irreducible representation which is compatible with the PBWfiltration arising from the famous PoincaréBirkhoffWitt theorem. This monomial basis is parametrized by the lattice points in a normal polytope, called the FeiginFourierLittelmannVinberg (FFLV) polytope. This construction solves a conjecture of E. Vinberg. In this talk, I will explain how to define quantum PBW filtrations on quantum groups, via realizing them as Hall algebras of quiver representations. In type A, for any finite dimensional irreducible representation, this construction leads to a canonical monomial basis, which is parametrized exactly by the FFLV polytope. If time permits, I will present results on other types. This talk is based on two joint works: one with G. Fourier and M. Reineke; the other with T. Backhaus and G. Fourier. 
Markus Reineke (Wuppertal)  Quiver moduli and small resolutions of some GIT quotients
7th November 2015, 1:00pm to 2:00pm  Show/hide abstractAbstract: A resolution of singularities of a singular space is called small if it satisfies a specific strong dimension estimate for its fibres. The utility of this notion stems from the fact that the intersection cohomology of a singular space can be computed from the cohomology of a small resolution. We construct a class of small resolutions using moduli spaces of representations of quiver. Several classes of examples will be discussed, related to determinantal varieties, moduli of point configurations in the projective line, and certain quotients by Levi actions. 
Welcome
8th April 2016, 2:30pm to 3:00pm 
Sira Gratz (University of Oxford)  Torsion pairs in discrete cluster categories
8th April 2016, 3:00pm to 4:00pm discrete cluster categories  Show/hide abstractAbstract: Igusa and Todorov introduced discrete cluster categories of Dynkin type A, which generally are of infinite rank. That is, their clusters contain infinitely many pairwise nonisomorphic indecomposable objects. In joint work with Holm and Joergensen we study torsion pairs in these categories and provide a complete combinatorial classification. Cluster tilting subcategories, tstructures, and co tstructures are all particular instances of torsion pairs and from our classification we are able to describe each of these classes. In particular, there are no co tstructures but, contrary to the finite case, there are a number of interesting tstructures. 
Drew Duffield (University of Leicester)  AuslanderReiten Components of Brauer Graph Algebras
8th April 2016, 4:30pm to 5:30pm  Show/hide abstractAbstract: One approach to the representation theory of algebras is to study the module category of an algebra. This can be achieved, at least in part, by describing the indecomposable modules of an algebra and the irreducible morphisms between them. The AuslanderReiten quiver of an algebra is a means of presenting this information. Of particular interest is a class of algebras known as Brauer graph algebras. These are symmetric special biserial algebras that have a presentation in the form of a (decorated) ribbon graph called a Brauer graph. An interesting feature of Brauer graph algebras is that one can often read off aspects of the representation theory by performing a series of combinatorial games on the Brauer graph, which removes the need for potentially difficult and lengthy calculations. The purpose of this talk is show that one can read off information regarding the AuslanderReiten theory of a Brauer graph algebra from its underlying Brauer graph. We begin by providing an algorithm for constructing the stable AuslanderReiten component containing a given indecomposable module of a Brauer graph algebra using only information from its Brauer graph. We then show that the structure of the AuslanderReiten quiver is closely related to the distinct Green walks around the Brauer graph and detail the relationship between the precise shape of the stable AuslanderReiten components for domestic Brauer graph algebras and their underlying graph. Furthermore, we show that the specific component containing a given simple or indecomposable projective module for any Brauer graph algebra is determined by the edge in the Brauer graph associated to the module. 
Short talk session
8th April 2016, 5:40pm to 6:40pm 
Dinner
8th April 2016, 7:00pm to 9:00pm Balbir's  Show/hide abstractAbstract: balbirs.co.uk 
Oliver King (University of Leeds)  Constructing some central idempotents in the Brauer algebra
9th April 2016, 9:30am to 10:30am  Show/hide abstractAbstract: Classical SchurWeyl duality relates the representations of the general linear group and the symmetric group via their action on tensor space. The Brauer algebra was introduced by Brauer in 1937, to play the role of the symmetric group when one replaces the general linear group with the orthogonal or symplectic groups. In this seminar I will briefly discuss the representation theory of the Brauer algebra, and then provide a new method of constructing central idempotents relating to the splitting of short exact sequences. I will then explain how we can derive some information about the Brauer algebra from these idempotents. 
Rosie Laking (University of Manchester)  The KrullGabriel dimension of a category
9th April 2016, 10:45am to 11:45am  Show/hide abstractAbstract: In this talk we will consider categories of finitely presented functors from a module category to the category of abelian groups. Such categories turn out to be a natural setting in which we may study the morphisms between finitely presented modules and the KrullGabriel dimension can be seen as a measure of the complexity of the morphism structure in the module category. It is calculated via iterated localisation of the functor category and we will give lots of examples in the context of finitedimensional algebras in order to demonstrate how the KrullGabriel dimension effectively reflects the structure of the module category. In particular I will report on joint work with K. Arnesen, D. Pauksztello, and M. Prest as well as joint work with M. Prest and G. Puninski. 
Lunch (sandwiches provided)
9th April 2016, 11:45am to 1:00pm 
Thomas BookerPrice (University of Lancaster)  Graded Cluster Algebras
9th April 2016, 1:00pm to 2:00pm  Show/hide abstractAbstract: A graded cluster algebra assigns degrees to the initial cluster variables in such a way that all exchange relations are homogeneous. This in turn makes all other cluster variables homogeneous and gives the cluster algebra the structure of a Z^ngraded algebra. These gradings have been implicit in the literature for some time, but were formalised (in the sense we are interested in) by Grabowski and Launois in 2013. One question we may ask about such a grading is how the cluster variables are distributed in terms of degrees: whether there are finitely many cluster variables per occurring degree, infinitely many per degree, or a mixture. In this talk we will give a partial classification of graded cluster algebras generated by rank 3 quivers in terms of this question. We will also consider the graded (quantum) cluster algebra structure on the homogeneous coordinate ring of m x n matrices and of quantum Grassmannians, and show that these contain cluster variables in all positive integer degrees. 
Time for individual discussions (as desired)
9th April 2016, 2:00pm to 3:30pm 
Vanessa Miemietz (East Anglia)  Baby steps in pdg 2representation theory
1st September 2016, 2:00pm to 3:00pm  Show/hide abstractAbstract: TBA 
Martin Herschend (Uppsala)  Thick subcategories of ncluster tilting subcategories
1st September 2016, 3:10pm to 4:10pm  Show/hide abstractAbstract: In Iyama's higher dimensional AuslanderReiten theory one shifts attention from module categories of algebras to so called ncluster tilting subcategories for some fixed positive integer n. These are nabelian (in the sense of Jasso) and so notions like kernel, cokernel and extension are replaced by their higher analogues: nkernel, ncokernel and nextension, which are similar except that the exact sequences involved are longer. Thus it makes sense to consider subcategories of nabelian categories that are closed under nkernels, ncokernels and nextensions. We shall refer to these as thick subcategories. In my talk I will present a characterization of thick subcategories of ncluster tilting subcategories with finitely many indecomposables. This will then be used to classify thick subcategories on ncluster tilting subacategories for Nakayama algebras of global dimension n. 
Catharina Stroppel (Bonn)  Rmatrices 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 Rmatrices 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 Ainfinity and tubes in higher AuslanderReiten 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 Ainfinity and of the tubes from the viewpoint of Iyama's higher AuslanderReiten 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 setup. 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 CohenMacaulay 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 CohenMacaulay clustertilting Bmodule, i.e. that it is a clustertilted 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. 
Alice Rizzardo (Edinburgh)  From Fourier transforms to FourierMukai functors
10th November 2016, 1:00pm to 1:50pm Lab 2, Postgraduate Statistics Centre, Lancaster University  Show/hide abstractAbstract: Starting from familiar concepts coming from analysis and classical algebraic geometry, I will introduce FourierMukai functors in the context of derived categories. I will explain what makes them useful, and talk about which functors between derived categories can be expressed in FourierMukai form. This is joint work with Michel Van den Bergh. 
Kevin de Laet (Antwerp)  Representation theory of Sklyanin algebras at points of finite order
10th November 2016, 2:00pm to 2:50pm Lab 2, Postgraduate Statistics Centre, Lancaster University  Show/hide abstractAbstract: Sklyanin algebras form a 2dimensional family of noncommutative algebras and they form deformations of the commutative polynomial ring. They depend on an elliptic curve E and a point t of E. In the case that t is a torsion point, Tate and Van den Bergh showed that such a Sklyanin algebra is a finite module over its center. However, except in the 3dimensional and in the 4dimensional case, the PIdegree and a description of the center is not known. After recalling the connection between fat point modules and irreducible representations for Sklyanin algebras, I will show that Sklyanin algebras at points of order 2 of odd global dimension n are Clifford algebras over a polynomial ring in n variables, which gives the PIdegree in this special case. For n=5 in this special case, the ramification locus is calculated, as well as the correspondence between fat points and points projective 4space. 
Tea and coffee
10th November 2016, 3:00pm to 3:30pm B Floor Social Area, Postgraduate Statistics Centre, Lancaster University 
Kenny de Commer (Brussels)  Torsionfreeness for discrete quantum groups
10th November 2016, 3:30pm to 4:20pm A54 Lecture Theatre, Postgraduate Statistics Centre, Lancaster University  Show/hide abstractAbstract: In order to formulate the BaumConnes conjecture in the setting of discrete quantum groups, R. Meyer introduced a notion of torsionfreeness for them. In this talk, we define torsionfreeness for rigid tensor C*categories and fusion rings. As an application, we then show that the discrete duals of the free unitary quantum groups of Wang and Van Daele are torsionfree, answering a question of C. Voigt. This is joint work with Y. Arano. 
Dinner
10th November 2016, 7:00pm to 9:00pm Paulo Gianni's, 15 New Street, Lancaster LA1 1EG, UK 
Iva Halacheva (Lancaster)  The cactus group, crystals, and shift of argument algebras
11th November 2016, 9:30am to 10:20am Lab 2, Postgraduate Statistics Centre, Lancaster University  Show/hide abstractAbstract: Two objects arising from a finitedimensional reductive Lie algebra g and its representation theory are the cactus group defined using the Dynkin diagram of g, and crystals encoding the information of grepresentations. We define an action of the cactus group on any crystal, which can be realized both combinatorially and geometrically. On one hand, it can be described in terms of Schützenberger involutions. On the other hand, it is the monodromy action for a covering of a certain moduli space, coming from a family of maximal commutative subalgebras of U(g) known as the shift of argument algebras. 
Tea and coffee
11th November 2016, 10:30am to 11:00am B Floor Social Area, Postgraduate Statistics Centre, Lancaster University 
David Jordan (Edinburgh)  The quantum Springer sheaf
11th November 2016, 11:00am to 11:50am A54 Lecture Theatre, Postgraduate Statistics Centre, Lancaster University  Show/hide abstractAbstract: In classical Springer theory, one is constructing representations of the Weyl group W of a reductive group, exploiting the geometry of the flag variety. Hotta and Kashiwara gave a striking reformulation of classical Springer theory, in terms of equivariant Dmodules on the Lie algebra g (i.e. systems of differential equations on g, with strong symmetry properties). In this talk, I'll review Hotta and Kashiwara's construction, and explain some joint work with Monica Vazirani to define and compute analogs of HottaKashiwara's Dmodules in the setting of quantum groups.
Registration and accommodation:
Please register here if you plan to attend: https://docs.google.com/forms/d/1izagapJpZaZf7qBpkXcwz6ltuldRJu8muyagLSiPk/viewform?usp=send_form
There is funding available for Ph.D. students and early career researchers.