# 40th ARTIN meeting

### University of Sheffield, Friday 9th and Saturday 10th of May 2014.

The 40th ARTIN meeting will be hosted at the School of Mathematics and Statistics of University of Sheffield on Friday 9th and Saturday 10th of May 2014. It will be funded by the London Mathematical Society and Glasgow Mathematical Journal Trust.

#### Schedule:

##### Friday 9th May Hicks Building LT3

**14:30-15:30 James Griffin (Glasgow): Moduli spaces of labelled graphs.**The automorphism groups of free groups and more generally free products are closely related to categories of graphs. This can be made precise both in algebraic topology, where the nerves of the categories are classifying spaces for the automorphism groups; and in representation theory, where functors from graphs to vector spaces can be induced to representations of the automorphism groups. I will discuss both and their relationship with Kontsevich's graph homology.

**16:00-17:00 Behrang Noohi (Queen Mary, Univ. of London): Lie theory for 2-groups.**Lie theory studies Lie groups, Lie algebras, and the relation between them. Motivated by recent developments in higher geometry, many aspects of Lie theory have been extended to Lie n-groups and Lie n-algebras. The case n=2 is particularly interesting and, as it turns out, can be formulated in elementary terms, without resorting to the heavy machinery of higher categories. In this talk I will discuss some of the main results in Lie theory of 2-groups (eg, Lie's main theorems).

##### Saturday 10th May Hicks Building LT3

**9:00-10:00 John Huerta (Lisbon): Trigroups and M-theory.**A trigroup is a tricategory on one object, with morphisms at all levels weakly invertible. We will discuss a trigroup coming from M-theory, the still mysterious branch of physics believed to unite all string theories.

**10:30-11:30 Dmitry Roytenberg (MPIM Bonn): Equivalence of models of "up to homotopy" algebras of differentiable functions.**Whereas coordinate rings of algebraic varieties are commutative algebras, coordinate rings of differentiable manifolds have an important extra structure: they are so-called C-infinity algebras. In the derived setting, coordinate rings additionally acquire a homotopy type; thus, coordinate rings of derived manifolds can be modeled either by simplicial C-infinity algebras, or "differential graded" ones (understood in an appropriate sense). We construct a Quillen equivalence between these two models in a conceptually elegant way, using finite Grassmann algebras as a "kernel". This generalizes and sheds new light on an old result of Quillen about commutative algebras and Lie algebras.

**11:45-12:45 Jacob Rasmussen (Cambridge): Torus knots and the rational DAHA.**I'll first describe a connection between finite dimensional representatations of rational Cherednik algebras of type A and an object of interest to topologists: the HOMFLY polynomial of the (m,n) torus knot and its categorification. Then I'll discuss the algebra and geometry which we think underlies this correspondence. Joint work with E. Gorsky, A. Oblomkov, and V. Shende.

#### Travel details:

Talks will be held in the Hicks Building at the University of Sheffield. Walking from the Sheffield train station to the University takes approximately 20 minutes, and there is also a tram that runs directly from the train station with a stop at the University very near the Hicks Building. The University of Sheffield travel advice webpage can be found here.

#### Accommodation and conference dinner:

There are a variety of hotels near the city centre of Sheffield. Here are three that guests of the University have used in the past (in order of increasing price).

There will be a conference dinner on Friday night.

#### Registration:

If you are intending to come, please contact Nick Gurski (nick.gurski@sheffield.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".