Conference in honour of
Olivier Mathieu's 60th birthday

Michel Brion (University of Grenoble)

Automorphisms of projective varieties

The talk will discuss which groups occur as automorphism groups of normal projective varieties. The main result asserts that every smooth connected group scheme over a field is the connected automorphism group of such a variety. The corresponding statement for Lie algebras is an open question in positive characteristic.

Stephen Donkin (University of York)

TBA

Vyacheslav Futorny (University of Sao Paulo)

Localization technique in representation theory

Localization functors, introduced by V. Deodhar, are important tools in the representation theory. They were used successfully by O. Mathieu for the classification of simple torsion free modules with finite-dimensional weight spaces over complex simple Lie algebras. Localization with respect to a simple root of Lie algebra is well understood, thanks to the results of H. Andersen, S. Arkhipov, K. Stroppel and others. Developing the ideas of O. Mathieu, we consider localization of the category O with respect to an arbitrary non-simple root. This allows to construct explicitly a large new class of simple modules together with their geometric realization. The talk is based on joint results with Libor Krizka.

Stéphane Gaussent (University of Saint-Étienne)

TBA

Seok-Jin Kang (Korea Research Institute of Arts and Mathematics)

Quantum Borcherds-Bozec algebras and their integrable representations

We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a triangular decomposition and the category of integrable representations is semi-simple.

Iryna Kashuba (University of Sao Paulo)

TBA

Peter Littelmann (University of Cologne)

TBA

Consuelo Martínez Lopéz (University of Oviedo)

TBA

Colette Moeglin (Institut de mathématiques de Jussieu)

TBA

Jacob Mostovoy (CINVESTAV-IPN)

TBA

Arturo Pianzola (University of Alberta)

Applications of non-abelian cohomology to infinite dimensional Lie theory (a survey of the last 20 years)

Many infinite dimensional mathematical objects, such as affine Kac-Moody Lie algebras, Extended Affine Lie Algebras, Quantum Groups and Superconformal algebras, can be thought as being of finite type by considering them as objects over a ring (the centroid of the object) and not the given base field. This simple observation allows that powerful theory of Reductive Group Schemes developed by Demazure and Grothendieck to enter into the picture. During the talk I will explain how this beautiful connection takes place, and illustrate many of the important results that have been established using this methods.

Marc Rosso (Institut de mathématiques de Jussieu)

TBA

Wilberd van der Kallen (University of Utrecht)

Reductivity properties over an affine base

When the base ring is not a field, power reductivity of a group scheme is a basic notion, intimately tied with finite generation of subrings of invariants. Geometric reductivity is weaker and less pertinent in this context. We give a survey of these properties and their connections.

Raika Dehy (Université Cergy-Pontoise) Benoît Dejoncheere (University of Alberta) Lucas Fresse (Université de Lorraine) Jérôme Germoni (Institut Camille Jordan, Lyon) Rosane Ushirobira (Inria, Lille) Rupert Yu (Université de Reims Champagne Ardenne)