08:30 to 09:55 Registration 09:55 to 10:00 Welcome - Ben Mestel INI 1 10:00 to 11:00 J Brundan ([Oregon])Blocks of the general linear supergroup I will relate the endomorphism algebra of a minimal projective generator for a block of the general linear supergroup to a limiting version of Khovanov's diagram algebra. One consequence is that blocks of the general linear supergroup are Koszul, in the same spirit as classical work of Beilinson, Ginzburg and Soergel on blocks of the BGG category O for a semisimple Lie algebra. This is joint work with Catharina Stroppel. INI 1 11:00 to 11:30 Coffee and Posters 11:30 to 12:30 EM Opdam ([Amsterdam])Spectral transfer category of affine Hecke algebras We introduce a notion of a spectral transfer morphism'' between affine Hecke algebras. Such a spectral transfer morphism from H_1 to H_2 is not given by an algebra homomorphism from H_1 to H_2 but rather by a homomorphism from the center Z_2 of H_2 to the center Z_1 of H_1 which is required to be compatible'' in a certain way with the Harish-Chandra \mu-functions on Z_1 and Z_2. The main property of such a transfer morphism is that it induces a correspondence between the tempered spectra of H_1 and H_2 which respects the canonical spectral measures (Plancherel measures''), up to a locally constant factor with values in the rational numbers. The category of smooth unipotent representations of a connected split simple p-adic group of adjoint type G(F) is Morita equivalent to a direct sum R of affine Hecke algebras. It is a remarkable fact that R admits an essentially unique spectral transfer morphism'' to the Iwahori-Matsumoto Hecke algebra of G. This fact offers a new perspective on Reeder's classification of unipotent characters for exceptional split groups which works in the general case, leading to an alternative approach to Lusztig's classification of unipotent characters of G(F). INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 P Achar ([Louisiana State])Staggered sheaves Let X be a variety endowed with an action of an algebraic group G acting with finitely many orbits. "Staggered sheaves" are certain complexes of G-equivariant coherent sheaves on X, generalizing the "perverse coherent sheaves" of Deligne and Bezrukavnikov. They form an abelian category that has many remarkable algebraic properties resembling those of l-adic perverse sheaves. In particular, this category is quasi-hereditary and admits a mixed structure. If time permits, I will describe some small examples. Some of these results are joint work with David Treumann. INI 1 15:00 to 15:30 Tea and Posters 15:30 to 16:30 V Toledano-Laredo ([Northeastern])Stability conditions and Stokes factors I will explain how the wall-crossing formulae studied by D. Joyce in the context of an abelian category A can be understood as Stokes phenomena for a connection on the Riemann sphere having an irregular singularity at 0 and values in the Ringel-Hall Lie algebra of A. This allows one to interpret Joyce's holomorphic generating functions as defining an isomonodromic family of such connections on the space of stability conditions of A. This is a joint work with Tom Bridgeland. INI 1 16:30 to 17:30 R Rouquier ([Oxford])Higher representations: geometry and tensor structures We will discuss the geometrical realisation of simple 2-representations of symmetric Kac-Moody algebras and their tensor products on one hand, and the algebraic construction of tensor products on the other hand. INI 1 17:30 to 18:30 Wine reception and Poster Session 18:45 to 19:30 Dinner at Wolfson Court
 09:00 to 10:00 S Ariki ([Kyoto])Graded q-Schur algebras Just 10 years ago, the decomposition matrix theorem for cyclotomic Hecke algebras was generalized to the decomposition matrix theorem for the q-Schur algebra by Varagnolo and Vasserot. This year, Brundan and Kleshchev proved graded analogue of the decomposition matrix theorem for cyclotomic Hecke algebras. Hence it is natural to give graded analogue of the decomposition matrix theorem for the q-Schur algebra. This may be done by defining appropriate setting for the graded version, and following ideas of Hemmer and Nakano, and Leclerc. INI 1 10:00 to 11:00 E Friedlander ([Southern California])Investigating $kG$-modules using nilpotent operators This is a report of on-going work with Jon Carlson, Julia Pevtsova, and Andrei Suslin. Our object of study is the representation theory of $kG$ where $G$ is a finite group scheme. Following Quillen's early work, first invariants involve cohomology and cohomological support varieties. These have interpretations in terms of 1-parameter subgroups and $\pi$-points. Finer invariants arise from considering the Jordan type of nilpotent operators, leading to local Jordan types, generalized support varieties, and algebraic vector bundles on projective varieties. INI 1 11:00 to 11:30 Coffee and Posters 11:30 to 12:30 P Fiebig ([Freiburg])Lusztig's conjecture as a moment graph problem To any root system we associate a labelled, partially ordered graph and a sheaf theory on the graph with coefficients in an arbitrary field k. An extension property then leads to the definition of a certain universal class of sheaves, the Braden-MacPherson sheaves. We formulate a conjecture about the multiplicity of their stalks. This conjecture implies Lusztig's conjecture on the irreducible characters of the simply connected algebraic group over k associated to the root system. Finally we list the proven instances of the conjecture. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 D Nakano ([Georgia])Atypicality, complexity and module varieties for classical Lie superalgebras Let ${\frak g}={\frak g}_{\bar 0}\oplus {\frak g}_{\bar 1}$ be a classical Lie superalgebra and ${\mathcal F}$ be the category of finite dimensional ${\frak g}$-supermodules which are semisimple over ${\frak g}_{\bar 0}$. In this talk we investigate the homological properties of the category ${\mathcal F}$. In particular we prove that ${\mathcal F}$ is self-injective in the sense that all projective supermodules are injective. We also show that all supermodules in ${\mathcal F}$ admit a projective resolution with polynomial rate of growth and, hence, one can study complexity in $\mathcal{F}$. If ${\frak g}$ is a Type I Lie superalgebra we introduce support varieties which detect projectivity and are related to the associated varieties of Duflo and Serganova. If in addition ${\frak g}$ has a (strong) duality then we prove that the conditions of being tilting or projective are equivalent. INI 1 15:00 to 15:30 Tea and Posters 15:30 to 16:30 J Bernstein ([Tel Aviv])On Casselman-Wallach globalization theorem About 20 years ago B.Casselman and N.Wallach proved a remarkable theorem about representations of real reductive groups. Namely they proved that any Harish Chandra module $M$ for a group $G$ can be uniquely extended to a smooth Frechet representation $V$ of this group (they called this procedure "the canonical globalization"). Unfortunately their proof is quite involved. For this reason their result is not that well known as it should be. For the same reason some natural generalizations of this result (e.g. how to make such globalization in a family) could not be studied. In my lecture I will describe a new approach to this problem developed in a joint work by B. Kroetz and myself that is technically simpler and allows to investigate some related phenomena. INI 1 18:45 to 19:30 Dinner at Wolfson Court INI 1