BIREP – Representations of finite dimensional algebras at Bielefeld
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ICRA 2012 Conference

The ICRA 2012 conference was held from Monday, 13 August, to Friday, 17 August 2012, in the lecture hall H7 in the main university building (UHG) of Bielefeld University (maps are available on the Travel Information page). It consisted of talks given by the invited speakers and additional talks selected shortly before the conference on the basis of submitted abstracts.

Invited speakers were as follows:

There was also a special session dedicated to Ragnar-Olaf Buchweitz on the occasion of his 60th birthday. Another session was devoted to the development of computational methods in representation theory.

Detailed information on many of the talks is available via the list of talks and the detailed time tables.

Conference Programme Overview

For a better overview and easy reference, time tables containing all talks together with the respective talk titles are available as a pdf document (68 KB).

All lectures were held in the lecture halls of the main university building (UHG).

Monday
13 August		 Tuesday
14 August		 Wednesday
15 August		 Thursday
16 August		 Friday
17 August
8:30 – 9:00 Registration
9:00 – 9:50 Plenary Plenary Special
session
dedicated to
Ragnar-Olaf
Buchweitz		 Plenary Plenary
10:00 – 10:30 Plenary Plenary Plenary Plenary
Coffee break Coffee break
11:00 – 11:20 Parallel Parallel Parallel Parallel
11:30 – 11:50 Parallel Parallel Parallel Parallel
12:00 – 12:20 Parallel Parallel Parallel Parallel
Lunch break
Excursion
14:00 – 14:50 Plenary Plenary Plenary Plenary
15:00 – 15:30 Plenary Plenary Plenary Plenary
Coffee break Coffee break
16:00 – 16:20 Parallel Parallel Parallel Parallel
16:30 – 16:50 Parallel Parallel Parallel Parallel
17:00 – 17:20 Parallel Parallel Parallel Parallel
17:30 – 18:20 Plenary Plenary Plenary Plenary
18:30 – Welcome
reception
19:00 – Computer algebra
session
20:00 – Conference
dinner

Abstracts

Sergey Fomin (Ann Arbor)
Cluster structures in rings of SL3 invariants

The rings of polynomial SL(V)-invariants of configurations of vectors and linear forms in a k-dimensional complex vector space V have been explicitly described by Hermann Weyl in the 1930s. Each such ring conjecturally carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. In joint work with Pavlo Pylyavskyy, we describe and explore these cluster structures in the case k=3.

Hiraku Nakajima (Kyoto)
Monoidal categorification, revisited

In my previous 'monoidal categorification of cluster algebras' via perverse sheaves on graded quiver varieties, the definition of a coproduct is missing, except finite type cases. Thus the construction does not give a true monoidal category, though it gives a well-defined multiplication on the quantum Grothendieck group. I explain how to define the true monoidal category.

Julia Pevtsova (Seattle)
Elementary subalgebras of modular Lie algebras and vector bundles on projective varieties

Let g be a p-restricted Lie algebra. We call a subalgebra E of g "elementary" of rank r if it is an abelian Lie algebra with trivial p-restriction of dimension r. For a fixed r we consider a projective variety Er(g) that parameterizes all elementary subalgebras of g of rank r. This variety is a natural generalization of the rank variety introduced by Carlson for elementary abelian p-groups and the support variety for Lie algebras of Friedlander and Parshall.

I'll identify this projective variety in various classical cases. I'll also show how representations of g with special properties lead to constructions of families of vector bundles on Er(g), thereby extending the study of "modules of constant Jordan type" and their geometric applications to this more general context.

This is a joint work with Jon Carlson and Eric Friedlander.

Raphaël Rouquier (Oxford/Los Angeles)
2-Hopf algebras

We will give a definition of tensor categories with a coproduct, and construct such structures for 2-Kac-Moody algebras. This is done in the A-infinity setting. As a consequence, the 2-category of A-infinity 2-representations of Kac-Moody algebras is equipped with a closed monoidal structure.

Michel Van den Bergh (Hasselt)
Non-commutative resolutions of determinantal varieties

During the lecture I will discuss joint work with Ragnar Buchweitz and Graham Leuschke on the non-commutative resolution of determinantal varieties. We will show that such resolutions can be constructed in a characteristic free manner and we will discuss their properties. In particular we will give a explicit presentation by generators and relations.