Nicolás Andruskiewitsch (Córdoba, Argentina)
Title: On the finite generation of the cohomology of abelian extensions of Hopf algebras
Abstract: A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is shown that every quasi-split finite-dimensional Hopf algebra satisfies the finite generation cohomology conjecture of Etingof and Ostrik. This is applied to a family of pointed Hopf algebras in odd characteristic introduced by Angiono, Heckenberger and the first author, proving that they satisfy the aforementioned conjecture.
Michel Brion (Grenoble, France)
Title: Vector fields on algebraic varieties in positive characteristics
Abstract: In characteristic zero, it is known that a vector field on an algebraic variety lifts uniquely to its normalization, and admits a reduction of singularities in low dimension. Both results fail in positive characteristic. The talk will present a remedy to this, based on notions of equivariant normality and regularity.
Stephen Donkin (York, UK)
Title: Endomorphism algebras of Young permutation modules for Hecke algebras
Abstract: We consider endomorphism algebras of Young permutation modules for Hecke algebras of type A. In certain cases, including quantisations of the partition algebras, we describe the block distribution of the simple modules. We also describe certain equivalences between blocks, The methods involve descent from the representation theory of quantum general linear groups.
Vyacheslav Futorny (SUSTech, China)
Title: Representations of Lie algebra of Hamiltonian vector fields
Abstract: We will discuss the Shen-Larsson functor from the category of sp(2n)-modules to the category of modules over the Hamiltonian Lie algebra. This functor preserves irreducibility except in the finite number of cases. Applied to finite dimensional representations it gives cuspidal modules, extending well-known results for other Cartan type algebras. The talk is based on joint results with S. Tantubay.
Stéphane Gaussent (Saint-Etienne, France)
Title: On the tensor product of irreducible representations of Kac-Moody Lie algebras
Abstract: The representation theory of Kac-Moody Lie algebras over the complex numbers is a very active area of research since Kac and Moody introduced these Lie algebras. A lot of tools can be used in this context: crystal graphs, geometry of flag manifolds, KLR 2-categories... But some natural conjectures still remain open, for instance the Kostant conjecture or the Schur positivity conjecture. In this talk, I will report on a joint work with Rekha Biswal on the description of some irreducible components in the tensor product of two irreducible integral highest weight representations of a symmetrisable Kac-Moody Lie algebra.
Iryna Kashuba (SUSTech, China)
Title: The Jucys-Murphy method and fusion procedure for the Sergeev superalgebra
Abstract: We use the Jucys-Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra. We apply them to give a version of the seminormal form for the irreducible modules with an explicit construction of basis vectors. We show that the idempotents can also be obtained from a new version of the fusion procedure.
Anne Moreau (Paris-Saclay, France)
Title: TBA
Abstract: TBA
Arturo Pianzola (Alberta, Canada)
Title: Loop torsors
Abstract: TBA
Simon Riche (Clermont-Ferrand, France)
Title: Semiinfinite sheaves on affine flag varieties
Abstract: We will explain how, generalizing a construction of Gaitsgory, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that "models" sheaves on the corresponding semiinfinite flag variety, with coefficients in a field of positive characteristic, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld's compactification, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon.
Marc Rosso (IMJ, France)
Title: TBA
Abstract: TBA
Wolfgang Soergel (Freiburg, Germany)
Title: Six functors and their coherence
Abstract: I want to explain a somewhat down-to-earth formalism detailing in which way the various natural isomorphisms of the six functors formalism are compatible. I also want to discuss a natural setting for proper pushforward along "locally proper separated maps".
Shaobin Tan (Xiamen, China)
Title: Representations for extended affine Lie algebras and vertex algebras
Abstract: Extended affine Lie algebras are generalization of the finite dimensional Lie algebras and affine Kac-Moody algebras. The elliptic Lie algebras are extended affine Lie algebras of nullity two. We knew that the restricted modules for any untwisted affine Kac-Moody algebra are isomorphic to the modules for the associated affine vertex algebra, while the restricted modules for the twisted affine Kac-Moody algebra are isomorphic to the twisted modules for the affine vertex algebra. In this talk we will deal with the integrable representations of elliptic toroidal Lie algebras, and the vertex algebras associated with elliptic Lie algebras of maximal type.
