Conference

During the International Conference on Representations of Algebras established figures and young scientists interested in the topic gather to share and discuss the latests advancements on the area and related topics. The list of plenary speakers will include the following people:

• Nicolás Andruskiewitsch (Universidad Nacional de Córdoba)

• Karin Baur (University of Leeds and Universität Graz)

• Xiao Wu Chen (University of Science and Technology of China)

• Radha Kessar (City, University of London)

• Ivan Shestakov (Universidade de São Pablo)

• Bertrand Toën (Université de Toulouse)

ABSTRACT FOR CONFERENCES:

Nicolás Andruskiewitsch - On a family of Hopf algebras arising from finite-dimensional Nichols algebras of diagonal type

The classification of the finite-dimensional Nichols algebras of diagonal type, obtained by Heckenberger, can be organized in terms of Lie theory. Such Nichols algebras give rise to several classes of Hopf algebras. In the talk we will focus on a class introduced by Angiono and defined from families that depend on a parameter; this extends a construction by De Concini, Kac and Procesi. The class includes quantum super groups and characteristic 0 deformations of some Lie algebras in characteristic 2 and 3. We show that these algebras give rise to Poisson orders in the sense of Brown and Gordon and we describe the corresponding symplectic leaves.

This is joint work with Iván Angiono and Milen Yakimov.

Karin Baur - Module categories for coordinate rings of Grassmannians

The category of maximal Cohen-Macaulay modules over a certain quotient of a preprojective algebra is known to provide a categorification of Scott's cluster algebra structure of the coordinate ring of the Grassmannian. This category is of infinite type in general - we study these types. We show that it is a tubular category. This makes it a very interesting examples of categories of infinite types and allows us to characterise certain modules of small rank.

Joint work with Dusko Bogdanic, Jianrong Li and with Ana Garcia Elsener.

Xiao Wu Chen - An invitation to the singular Yoneda dg category

This is an introduction to a new dg category associated to any algebra, called the singular Yoneda dg category; it is a singular analogue of the Yoneda dg category (implicitly due to Keller), and provides a new dg enhancement for the singularity category. Using this explicit dg enhancement, we describe the singularity category of a finite dimensional algebra using the dg Leavitt path algebra of its radical quiver. The Hom complexes in the singular Yoneda dg category are related to the stabilization functor in the sense of Krause. This is based on joint work with Zhengfang Wang.

Radha Kessar - On Hochschild cohomology of symmetric groups and generating functions.

I will report on recent joint work with Dave Benson and Markus Linckelmann on computing dimensions of the Hochschild cohomology groups

of symmetric groups.

Ivan Shestakov - The structure and representations of Jordan superalgebras.

This will be a survey on the structure and representations of Jordan superalgebras.

Bertrand Toën - Algebraic foliations and derived geometry (joint work with G. Vezzosi)

Foliations defined on algebraic varieties are rarely without singularities. These singularities can be studied using derived techniques via a notion of "derived foliations", in the same way than singularities of algebraic varieties can be studied using the notion of derived schemes. In this talk, I will explain the notion of derived foliations and report on recent applications for the study of singular foliations. These include results in the complex case, as well as foliations defined over base fields of arbitrary characteristics.