### 39th ARTIN meeting

#### Newcastle University, Friday 28th and Saturday 29th of March 2014.

The 39th ARTIN meeting will be hosted at the School of Mathematics and Statistics of Newcastle University on Friday 28th and Saturday 29th of March 2014. The meeting is organized by **Martina Balagovic**, and will feature talks by post-docs and post-grads. It will be funded by the London Mathematical Society and Glasgow Mathematical Journal Trust.

#### Schedule:

##### Friday 28th March Armstrong Building ARMB.3.38

**14-15 Antonio Sartori (York): (Super) skew Howe duality and categorification.**Skew Howe duality is a classical tool which relates the representation theory of the Lie algebras gl(n) and gl(r). In a certain sense, it extends Schur-Weyl duality, and it has been proven very useful to construct a graphical calculus for link invariants and for their categorification. In my talk, I will explain how the BGG category O provides a categorification of skew Howe duality, and how this can be modified in order to obtain a super version, by going through several interesting issues and some open questions.

**15:30-16:30 Ana Rovi (Glasgow): Lie-Rinehart algebras, Hopf algebroids with and without an antipode.**Through the process of horizontal categorification (or oidification), Lie groups become Lie groupoids, Lie algebras become Lie algebroids (Lie-Rinehart algebras) and Hopf algebras correspond to Hopf algebroids. Since the enveloping algebra of a Lie algebra is a Hopf algebra, it is a natural question whether the enveloping algebra of a Lie-Rinehart algebra carries the structure of a Hopf algebroid. In this talk I will give some background on these structures, and will give examples of Hopf algebroids without an antipode. Some of these examples and results are joint work with Uli Kraehmer.

**16:45-17:45 Sian Fryer (Manchester): The q-Division Ring: Fixed Rings and Automorphisms.**The q-division ring (denoted here by D) is one of the easiest examples of noncommutative infinite dimensional division rings to define, but answering even fairly basic questions concerning the structure of its automorphism group or its sub-division rings of finite index is still quite difficult. The second question in particular is of interest due to its connections with Artin's conjectured classification of surfaces in non-commutative algebraic geometry. I will describe the structure of the fixed rings of D for a certain class of finite groups and use this to construct some rather unexpected examples of homomorphisms on D, including a conjugation automorphism which is not inner and a conjugation homomorphism which is not even bijective.

##### Saturday 29th March Herschel Building HERB.4.TR3

**9-10 Aaron Chan (Aberdeen): Simple-minded system in triangulated categories.**The stable module category of an artinian algebra has the same object as the module category, but hom-spaces are quotiented out by morphisms which factor through projective modules. This construction effectively turns projective modules into zero. The lack of "projective-minded" objects is the main obstacle in studying the stable module categories and equivalences between them. Koenig and Liu introduced the simple-minded system as a new attempt to understand stable module categories and stable equivalences. This notion was extended to certain triangulated categories by Dugas. In this talk, I will introduce the simple-minded systems following Dugas approach, and present some classification results for stable module categories of representation-finite self-injective algebras, and triangulated orbit categories of the bounded derived categories of representation-finite hereditary algebras. This talk contains material in a joint work with Koenig and Liu.

**10:30-11:30 Julia Sauter (Leeds and Bielefeld): Springer Theory methods in Representation Theory.**Classical Springer Theory is a geometric construction of Weyl group algebras together with their simple representations. A similar construction leads to KLR-algebras whose graded projective modules categorify the upper half of the quantum group (of a given quiver), by work of Khovanov, Lauda and others. We explain these constructions more generally. As a further application we give a geometric construction of the Hall module (defined by Matthew Young).

**11:45-12:45 Noah White (Edinburgh): The center of quantum GL_n.**Centers of enveloping algebras of Lie algebras and their quantisations have attracted a lot of attention in the literature. I will give an account of some of these descriptions including one due to Reshetikhin using the graphical calculus of braided categories. I will also describe some joint work with David Jordan on giving elementary combinatorial formulas for free generators of the center.

##### Travel details:

The meeting will take place at Newcastle University, which is in the city center of Newcastle, 15 minutes walk from the Central Railway Station. For maps and information how to get here, please see here.

##### Conference dinner:

There will be a conference dinner near the hotel on Friday.

##### Registration:

If you are intending to come, please contact Martina Balagovic (martina.balagovic@newcastle.ac.uk).

If you have PhD students or colleagues who might be interested, please encourage them to attend. If you would like to subscribe to the ARTIN mailing list, please send an email to sympa at mlist.is.ed.ac.uk, with subject line: "subscribe artin first_name last_name".