# 42nd ARTIN meeting

### University of Glasgow, Friday 7th and Saturday 8th of November 2014.

The 42nd ARTIN meeting will be hosted at the School of Mathematics and Statistics of University of Glasgow on Friday 7th and Saturday 8th of November 2014. It will be funded by the London Mathematical Society and Glasgow Mathematical Journal Trust. ARTIN attendees are also welcome to attend the NBGGT (North British Geometric Group Theory) meeting also being hosted at Glasgow on the same two days. For information about NBGGT and a schedule of talks, see the following: Schedule for NBGGT talks.

Friday,

**15:00-16:00:**Sian Fryer, Leeds**16:00-16:30:**Tea/Coffee in Common Room**17:30-18:30:**William Crawley-Boevey, Leeds

Saturday,

**10:30-11:00:**Tea/Coffee**11:00-12:00:**Stephane Launois, Kent

All talks will take place in lecture room 204 of the mathematics building.

Titles and abstracts:

**Bill Crawley-Boevey**(Leeds)

**Title: Two applications of the functorial filtration method**
**Abstract:** The method in question is the one used by Gelfand and Ponomarev in the classification of annihilating operators (to which they reduced the classification of certain indecomposable representations of the Lorentz group). It was further developed by Gabriel, and used by Ringel to classify indecomposable representations of dihedral groups. In the functorial filtration method one shows that a candidate list of indecomposable representations is complete by writing down two explicit vector space filtrations of a representation and verifying certain compatibilities between the list and the filtrations. I will discuss the use of this method in the following two cases: (1) the classification of finitely generated modules for infinite dimensional string algebras such as kx,y/(xy), and (2) the classification of persistence modules, that is, functors from a totally ordered set, considered in the natural way as a category, to the category of vector spaces. Such modules arise in the study of persistent homology.

**Sian Fryer**(Manchester/Leeds)

**Title: Division Rings as Deformations of Commutative Function Fields**
**Abstract:** One of the big open problems in non-commutative algebraic geometry is the classification of the non-commutative surfaces up to birational equivalence, i.e. isomorphism of their function fields. These function fields are (loosely speaking) division rings of transcendence degree 2, so the question can be rephrased purely in terms of ring theory: can we find any new division rings with the right sort of properties?

One way to investigate this is to look at sub-division rings of finite index within existing rings and describe their ring structure; however, doing any sort of computations with non-commutative fractions quickly becomes infeasible and makes attacking the problem directly quite difficult. Instead we can try to approach the question from another direction, by viewing the division rings as deformations of a commutative function field endowed with a Poisson bracket which preserves a "first order impression" of the division ring's non-commutative multiplication. Focusing on the division ring of the quantum plane, I will talk about how we can try to use this idea to say something about the structure of certain subrings of this ring.

**Stephane Launois**(Kent)

**Title: On the Poisson Dixmier-Moeglin Equivalence**
**Abstract:** Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this talk I will discuss this question.

There will be space and time set aside Saturday afternoon for informal discussions, so this is a great opportunity to meet up with collaborators past, present and future.

Directions to get to the maths building at Glasgow can be found here and here (Maths is D4 on the Gilmorehill Campus Map).

Please register at this page if you plan to attend.

If you have any questions, feel free to contact Gwyn Bellamy at gwyn.bellamy "at" glasgow dot ac dot uk.