TITLESABSTRACTS
 Sergey ARKHIPOV
 Braid group action on equivariant matrix factorizations
 Abstract. Given an algebraic variety X acted on by a simple algebraic group G, we define a certain category of matrix factorizations on the product of the cotangent bundle to X and of the Borel subalgebra in Lie(G). The potential is provided by the moment map. We construct a categorical braid group action on the corresponding derived category. The well known construction of Bezrukavnikov and Riche appears to be a specialization of ours for X being a point.
 David BENZVI
 Elliptic Character Sheaves
 Abstract. I will describe two dual approaches to character sheaves for loop groups via Geometric Langlands of the twotorus. The spectral approach (appearing in preprints 1312.7164, 1312.7164) involves the Bmodel of the Hitchin system of a twotorus. The automorphic approach (initial steps appearing in 1302.7053) involves the Amodel of the dual Hitchin system. I will emphasize relations to topological field theory and trace formulae. The results intertwine various strands joint with D. Nadler, A. Preygel and P. Li (Berkeley).
 Pavel ETINGOF
 Dmodules on Poisson varieties, Poisson homology, and symplectic resolutions
 Abstract. Let X be an affine Poisson algebraic variety over complex numbers with finitely many symplectic leaves.
Then the zeroth Poisson homology O(X)/{O(X),O(X)} is finite dimensional. This has applications to representation theory
(if A is a filtered quantization of O(X) then A has finitely many irreducible finite dimensional representations). The proof
is based on attaching to X a right Dmodule M(X) on X which is the quotient of the canonical Dmodule D(X)
on X by the action of hamiltonian vector fields, and showing that it is holonomic, and that the zeroth Poisson homology
of X is just the underived direct image of M(X) to the point. This motivates considering the full direct image of M(X)
in the more general case when X is not necessarily affine. This direct image is called the Poissonde Rham homology of X.
If X is symplectic, then M(X) is the canonical sheaf, and thus the Poissonde Rham homology coincides with the usual De Rham cohomology of X,
but in general the Poissonde Rham homology is hard to compute. However, if X has a symplectic resolution of singularities,
we conjectured with T. Schedler that the Poissonde Rham homology of X is isomorphic to the de Rham cohomology of the resolution.
I will explain the motivation for this conjecture, and describe a few cases when it is proved (symmetric powers of simple singularities, Springer fibers).
I will also describe some other cases (such as surfaces in C^3 with isolated singularities) when there is no symplectic resolution but there is a smooth
symplectic deformation, and the Poissonde Rham homology equals the cohomology of the deformation.
Finally, I'll describe the structure of M(X) for isolated quasihomogeneous surface singularities. This is joint work with T. Schedler.

Victor GINZBURG
 Counting indecomposables over a finite field
 Abstract. We develop an alternative approach to the theorem
of Hausel, Letellier, and RodriguezVillages
on counting inddecomposable quiver representations.
Our approach is based on character sheaves and it
does not involve combinatorial tools.
A similar approach applies for counting indecomposable
vector bundles on an algebraic curve in terms of the
geometry of Higgs bundles. There seems to be a connection
with a recent work of Deligne on counting irreducible
local systems.

Sam GUNNINGHAM
 A conceptual approach to the generalized Springer correspondence.
 Abstract.
I will sketch a proof of the generalized Springer correspondence using a Mackey theorem on functors of
parabolic induction and restriction for perverse sheaves on the nilpotent cone. This approach allows
for substantial (further) generalizations; in particular, a description of the whole derived category
of adjoint equivariant Dmodules on a reductive Lie algebra (or algebraic group).

David JORDAN
 Quantizing character varieties via 4D TFT
 Abstract. The character variety $Ch_G(S)$ is a moduli space of representations of
$\pi_1(S)$ into G. When $G$ is reductive, $Ch_G(S)$ carries a canonical
Poisson bracket constructed by Goldman and AtiyahBott. The assignment
$S \mapsto Ch_G(S)$ is natural and fully local in $S$, and hence defines
a topological field theory $Ch_G$. In this talk, I'll explain joint
work with D. BenZvi and A. Brochier quantizing each $Ch_G(S)$
compatibly with its TFT structure, leading to a (3+1)dimensional TFT
$Ch^q_G$, which can be viewed as an extension to generic $q$ of the
ReshetikhinTuraev invariants.
Using tools of factorization homology and representation theory of
tensor categories, it is possible to give fairly complete computations
of $Ch^q_G(S)$. Familiar algebras, such as reflection equation
algebras, quantum differential operators, and double affine Hecke
algebras appear naturally in the computations.
 Daniel JUTEAU
 Finite dimensional representations of rational Cherednik algebras: a necessary condition
 Abstract. In joint work with Stephen Griffeth, Armin Gusenbauer and Martina Lanini, we give a necessary condition for a simple module of a rational Cherednik algebra (associated to an arbitrary complex reflection group, and for any choice of the $c$ parameter) to be finite dimensional.
 Kobi KREMNITZER
 Analytic geometry and representation theory
 Abstract. I will describe a new approach to analytic geometry (Archimedean and nonArchimedean). In this approach
analytic geometry is viewed as algebraic geometry relative to an appropriate category of topological vector spaces.
Using this one can develop analytic derived geometry and analytic Tannakian formalism. These tools can then be used
to develop analytic geometric representation theory. This is joint work
with Oren BenBassat.
 Ivan LOSEV
 Derived equivalences for Cherednik algebras
 Abstract. A Rational Cherednik algebra is constructed for every complex reflection
group and depend on a parameter that is a collection of complex numbers. For these
algebras, one can define categories O. Rouquier conjectured that two categories
O corresponding to parameters with integral difference are derived equivalent.
In my talk, I'll speak about the proof.
 Kevin MCGERTY
 Morse theory decomposition for categories of Dmodules on stacks
 Abstract. Motivated by the study of localisation theory for quantizations of Hamiltonian reductions,
we will describe an algebrogeometric version of Morse stratifications yields a recollement of the derived
category of Dmodules on algebraic stacks. Time permitting we will discuss work in progress on the relation
between this decomposition and the question of when the hyperKahler Kirwan map is surjective.
This is joint work with Prof. T. Nevins (UIUC).
 Simon RICHE
 Geometric Koszul duality for modular perverse sheaves on flag varieties
 Abstract.
I will report on a joint work with Pramod Achar which aims at describing some structural properties of the category of Bruhatconstructible perverse sheaves on the flag variety of a connected complex reductive group, with coefficients in a field of positive characteristic. In particular we construct a modular ``mixed derived category'', which allow us to construct a Koszul duality relating sheaves on our given flag variety with sheaves on the flag variety of the Langlands dual group. This Koszul duality exchanges tilting perverse sheaves and the parity sheaves of JuteauMautnerWilliamson.
 Laura RIDER
 Modular representation theory and the geometric Satake equivalence
 Abstract. The geometric Satake equivalence proven by MirkovicVilonen (building on work of Lusztig and Ginzburg)
allows one to study the representation theory of an algebraic group via the topology of the affine Grassmannian for
the Langlands dual group. It is hoped that the modular representation theory of an algebraic group may be understood
geometrically, with a key role played by a class of objects known as parity sheaves, defined by JuteauMautnerWilliamson.
In my talk, I will describe this dictionary between representation theory and geometry, with an emphasis on the
MirkovicVilonen conjecture, recently proven in joint work with Pramod Achar.
 Travis SCHEDLER
 Poissonde Rham homology of cones and special polynomials
 Abstract. This is a sequel to Etingof's talk and includes joint work
with Proudfoot. Given a Poisson cone, its Poissonde Rham homology has
an additional weight grading, coming from dilations of the cone. The
resulting twovariable Hilbert series recovers special polynomials:
for hypertoric varieties, this recovers the Tutte polynomial and a
polynomial defined by Denham using the combinatorial Laplacian. By a
conjecture of Lusztig, for Slodowy slices of the nilpotent cone, this
recovers Kostka polynomials. Along the way we will prove my
conjecture with Etingof in the hypertoric case (and, in
general, reduce it to a combinatorial statement involving slices of
symplectic leaves). If time permits, I will explain a related
conjecture with Etingof on the twovariable Hilbert series of
symplectic resolutions, and a conjecture of Proudfoot relating it to
symplectic duality.
 Peng SHAN
 Koszulity for category O of affine Lie algebras and rational Cherednik algebras
 Abstract. I will explain the standard Koszul property of a parabolic O of affine Lie algebras, and an equivalence of highest weight categories between affine parabolic category O for gl_n and the category O of cyclotomic rational Cherednik algebras. As an application, this gives the character formulae and standard Koszul property of the category O of cyclotomic rational Cherednik algebras. (Joint work with Raphael Rouquier, Michela Varagnolo and Eric Vasserot.)
 Wolfgang SOERGEL
 Unicity of the grading of category O
 Abstract. This is joint work with Michael Rottmaier.
I want to explain why the usual grading
of category O is uniquely caracterized by its compatibility
with the action of the center of the enveloping algebra,
and what in fact all these words mean.
 Geordie WILLIAMSON
 Global and local Hodge theory of Soergel bimodules
 Abstract. I will give an overview of the global and local Hodge theory (i.e. hard Lefschetz and HogdeRiemann bilinear relations) of Soergel bimodules. I will focus on interesting new aspects including the difficulty of determining the "hard Lefschetz locus" and the local intersection forms, which are a version for intersection cohomology version of the equivariant multiplicity. I will also try to explain the role played by the nil Hecke ring.