Videos and presentation materials from other INI events are also available.
Event  When  Speaker  Title  Presentation Material 

ALT 
5th February 2008 15:00 to 16:00 
Complete reducibility and rationality  
ALTW01 
12th January 2009 10:00 to 11:00 
P Achar 
Derived categories and perverse sheaves
Perverse sheaves are a very important and powerful tool in representation theory. In these talks, we will begin with the formalism of derived categories and tstructures, needed to define perverse sheaves. Next, we will go through the list of remarkable properties of perverse sheaves that make them "better" than ordinary sheaves, and are the source of their usefulness. Lastly, we will look at a couple of representation theory applications. (Some basic familiarity with ordinary sheaves may be a helpful prerequisite.)


ALTW01 
12th January 2009 11:30 to 12:30 
Hecke algebras at roots of unity
We discuss various issues around nonsemisimple Hecke algebras: cellular structure, James' conjecture, application to modular HarishChandra series for finite groups of Lie type.


ALTW01 
12th January 2009 14:00 to 15:00 
Categorification of sl(2)modules
The aim of this course is to introduce the KazhdanLusztig theory, in the general framework of unequal parameters. We plan to talk about Lusztig's Conjectures, the asymptotic algebra, and to give a detailed account on some examples (symmetric group, type B,...). If time is left, we might talk about the connections with Cherednik algebras, or with representations of finite reductive groups, or with the geometry of the flag variety, or with the computation of decomposition matrices using the canonical bases of the Fock space (at most one of these four topics will be treated).


ALTW01 
13th January 2009 09:00 to 10:00 
Symmetry, polynomials and quantisation  
ALTW01 
13th January 2009 10:00 to 11:00 
P Achar 
Derived categories and perverse sheaves
Perverse sheaves are a very important and powerful tool in representation theory. In these talks, we will begin with the formalism of derived categories and tstructures, needed to define perverse sheaves. Next, we will go through the list of remarkable properties of perverse sheaves that make them "better" than ordinary sheaves, and are the source of their usefulness. Lastly, we will look at a couple of representation theory applications. (Some basic familiarity with ordinary sheaves may be a helpful prerequisite.)


ALTW01 
13th January 2009 11:30 to 12:30 
Hecke algebras at roots of unity
We discuss various issues around nonsemisimple Hecke algebras: cellular structure, James' conjecture, application to modular HarishChandra series for finite groups of Lie type.


ALTW01 
13th January 2009 14:00 to 15:00 
A Kleshchev 
Walgebras and Hecke algebras 1
We discuss a new presentation for blocks of cyclotomic Hecke algebras which allows to grade these blocks. This opens up a way for studying graded representation theory of cyclotomic Hecke algebras. We give emphasis to the recent result of KhovanovLauda, Rouquier, BrundanKleshchev and KleshchevRam.


ALTW01 
14th January 2009 09:00 to 10:00 
Symmetry, polynomials and quantisation  
ALTW01 
14th January 2009 10:00 to 11:00 
P Achar  Derived categories and perverse sheaves  
ALTW01 
14th January 2009 11:30 to 12:30 
Hecke algebras at roots of unity
We discuss various issues around nonsemisimple Hecke algebras: cellular structure, James' conjecture, application to modular HarishChandra series for finite groups of Lie type.


ALTW01 
15th January 2009 09:00 to 10:00 
Symmetry, polynomials and quantisation  
ALTW01 
15th January 2009 10:00 to 11:00 
P Achar  Derived categories and perverse sheaves  
ALTW01 
15th January 2009 11:30 to 12:30 
Categorification of sl(2)modules  
ALTW01 
15th January 2009 14:00 to 15:00 
A Kleshchev 
Walgebras and Hecke algebras 2
We discuss a new presentation for blocks of cyclotomic Hecke algebras which allows to grade these blocks. This opens up a way for studying graded representation theory of cyclotomic Hecke algebras. We give emphasis to the recent result of KhovanovLauda, Rouquier, BrundanKleshchev and KleshchevRam.


ALTW01 
16th January 2009 09:00 to 10:00 
Symmetry, polynomials and quantisation  
ALTW01 
16th January 2009 10:00 to 11:00 
P Achar  Derived categories and perverse sheaves  
ALTW01 
16th January 2009 11:30 to 12:30 
Categorification of sl(2)modules  
ALTW01 
16th January 2009 14:00 to 15:00 
A Kleshchev 
Walgebras and Hecke algebras 3
We discuss a new presentation for blocks of cyclotomic Hecke algebras which allows to grade these blocks. This opens up a way for studying graded representation theory of cyclotomic Hecke algebras. We give emphasis to the recent result of KhovanovLauda, Rouquier, BrundanKleshchev and KleshchevRam.


ALTW01 
19th January 2009 09:00 to 10:00 
M Broué  Complex reflection groups and their associated braid groups and Hecke algebras  
ALTW01 
19th January 2009 10:00 to 11:00 
Introduction to KazhdanLusztig theory with unequal parameters  
ALTW01 
19th January 2009 11:30 to 12:30 
Higher representations of Lie algebras  
ALTW01 
19th January 2009 14:00 to 15:00 
D Vogan  Schubert varieties and representations of real reductive groups  
ALTW01 
20th January 2009 09:00 to 10:00 
M Broué  Complex reflection groups and their associated braid groups and Hecke algebras  
ALTW01 
20th January 2009 10:00 to 11:00 
Introduction to KazhdanLusztig theory with unequal parameters  
ALTW01 
20th January 2009 11:30 to 12:30 
Higher representations of Lie algebras  
ALTW01 
20th January 2009 14:00 to 15:00 
D Vogan  Schubert varieties and representations of real reductive groups  
ALTW01 
21st January 2009 09:00 to 10:00 
M Broué  Complex reflection groups and their associated braid groups and Hecke algebras  
ALTW01 
21st January 2009 10:00 to 11:00 
I Losev 
Finite Walgebras and their representations A (finite) Walgebra is a certain associative algebra constructed from a semisimple Lie algebra and its nilpotent element. The main reason why they are interesting is their relation to the representation theory of universal enveloping algebras. In this course I am going to explain two different definitions of Walgebras: by Hamiltonian reduction (Premet, GanGinzburg) and deformation quantization (I.L). Then I am going to explain category equivalence theorems relating representations of Walgebras and universal enveloping algebras and describe relation between primitive ideals. 

ALTW01 
21st January 2009 11:30 to 12:30 
Higher representations of Lie algebras  
ALTW01 
22nd January 2009 09:00 to 10:00 
I Losev 
Finite Walgebras and their representations A (finite) Walgebra is a certain associative algebra constructed from a semisimple Lie algebra and its nilpotent element. The main reason why they are interesting is their relation to the representation theory of universal enveloping algebras. In this course I am going to explain two different definitions of Walgebras: by Hamiltonian reduction (Premet, GanGinzburg) and deformation quantization (I.L). Then I am going to explain category equivalence theorems relating representations of Walgebras and universal enveloping algebras and describe relation between primitive ideals. 

ALTW01 
22nd January 2009 10:00 to 11:00 
Introduction to KazhdanLusztig theory with unequal parameters  
ALTW01 
22nd January 2009 11:30 to 12:30 
Higher representations of Lie algebras  
ALTW01 
22nd January 2009 14:00 to 15:00 
D Vogan  Schubert varieties and representations of real reductive groups  
ALTW01 
23rd January 2009 09:00 to 10:00 
I Losev 
Finite Walgebras and their representations A (finite) Walgebra is a certain associative algebra constructed from a semisimple Lie algebra and its nilpotent element. The main reason why they are interesting is their relation to the representation theory of universal enveloping algebras. In this course I am going to explain two different definitions of Walgebras: by Hamiltonian reduction (Premet, GanGinzburg) and deformation quantization (I.L). Then I am going to explain category equivalence theorems relating representations of Walgebras and universal enveloping algebras and describe relation between primitive ideals. 

ALTW01 
23rd January 2009 10:00 to 11:00 
Introduction to KazhdanLusztig theory with unequal parameters  
ALTW01 
23rd January 2009 11:30 to 12:30 
Higher representations of Lie algebras  
ALTW01 
23rd January 2009 14:00 to 15:00 
D Vogan  Schubert varieties and representations of real reductive groups  
ALT 
27th January 2009 15:00 to 16:00 
A Cox  Blocks and decomposition numbers for the Brauer algebra  
ALT 
29th January 2009 15:00 to 16:00 
Finite groups, black box groups, algebraic groups  
ALT 
5th February 2009 15:00 to 16:00 
Complete reducibility and rationality  
ALT 
10th February 2009 15:00 to 16:00 
Tits' centre conjecture for subgroups of algebraic groups  
ALT 
12th February 2009 15:00 to 16:00 
Combinatorics of KazhdanLusztig cells  
ALT 
17th February 2009 14:00 to 15:00 
S RyomHansen  On the denominators of Young's seminormal basis  
ALT 
17th February 2009 15:15 to 16:15 
K Brown  Hopf algebras of small GelfandKirillov dimension  
ALT 
19th February 2009 15:00 to 16:00 
D Hernandez  Gbundles on elliptic curves and quantum groups  
ALT 
24th February 2009 15:00 to 16:00 
On the representation of St when t is not a natural number  
ALT 
26th February 2009 10:00 to 11:00 
Nilpotent subalgebras of semisimple Lie algebras, some unexpected torsion  
ALT 
26th February 2009 11:15 to 12:15 
G Seitz  Unipotent and nilpotent elements in simple algebraic groups  
ALT 
3rd March 2009 14:00 to 15:00 
Convolution algebras: an explicit construction  
ALT 
3rd March 2009 15:15 to 16:15 
CM Ringel  Root systems and canonical algebras  
ALT 
5th March 2009 15:00 to 16:00 
Periodic automorphisms of semisimple Lie algebras  
ALT 
10th March 2009 14:00 to 15:00 
A Molev  LittlewoodRichardson polynomials  
ALT 
10th March 2009 15:15 to 16:15 
Exceptional sequences of invertible sheaves on rational surfaces  
ALT 
12th March 2009 15:00 to 16:00 
O Brunat  A basic set for the alternating group  
ALT 
17th March 2009 14:00 to 15:00 
Support spaces, Jordan types and indecomposable modules  
ALT 
17th March 2009 15:15 to 16:15 
The WeilSteinberg character of finite classical groups  
ALT 
19th March 2009 15:00 to 16:00 
Quasireductive Lie algebras  
ALTW02 
23rd March 2009 10:00 to 11:00 
Crystal structure for representations of Cherednik algebras
I will report on recent work of Peng Shan (Paris VII). Using the parabolic induction and restriction functors of Bezrukavnikov and Etingof she showed the existence of a crystal structure on category O of the rational Cherednik algebras of type G(m,1,n) as n varies. Independently, Maurizio Martino (Bonn) and I proved the same result, with a slightly different construction which I shall outline.


ALTW02 
23rd March 2009 11:30 to 12:30 
Yangians and Dorey's rule
We discuss finitedimensional representations of Yangians and quantum affine algebras. Dorey's rule can be viewed as an analog of the famous PRV conjecture proved by Kumar and Mathieu and predicts the multiplicity of the trivial representation in a tensor product of three fundamental representations of the Yangian.


ALTW02 
23rd March 2009 14:00 to 15:00 
WL Gan 
Dunkl operators for symplectic reflection algebras of wreathproduct types
I will speak on an analogue of Dunkl operators attached to wreathproduct of a symmetric group and a finite subgroup of SL(2,C). These operators are a main ingredient in the realization of the spherical subalgebra of symplectic reflection algebras of wreathproduct types by quantum hamiltonian reduction. This is a joint work with P. Etingof, V. Ginzburg and A. Oblomkov which appeared in Publ. Math IHES no. 105.


ALTW02 
23rd March 2009 15:30 to 16:30 
Affine Walgebras and Zhu's Poisson varieties associated with KacMoody vertex algebras
The C2 cofiniteness condition is an important finiteness condition on a vertex algebra which guarantees the finitedimensionality of the corresponding conformal blocks. In this talk I will talk about the relationship between the C2 cofiniteness condition of affine W algebras and the certain invariants of KacMoody vertex algebras.


ALTW02 
23rd March 2009 16:30 to 17:30 
E Ragoucy 
Nested Bethe ansatz for spin chains
We present in a unified way the nested Bethe ansatz for spin chains based on gl(n), gl(mn) and their deformations. We perform the ansatz for closed and open spin chains. In the case of open spin chains, we use diagonal boundary conditions. In all cases, we deduce a recursion formula, and a trace formula for Bethe vectors.


ALTW02 
24th March 2009 09:00 to 10:00 
Yangians, finite Walgebras and Hecke algebras
I'll talk about representations of finite Walgebras with special reference to the type A case, where there are interesting connections to Yangians and to cyclotomic Hecke algebras.


ALTW02 
24th March 2009 10:00 to 11:00 
D Rumynin 
Modular representations of Lie algebras
We will discuss geometric issues that appear in modular representation theory of simple Lie algebras.


ALTW02 
24th March 2009 11:30 to 12:30 
Equidimensionality of characteristic varieties over Cherednik algebras
This talk will report on joint work with Victor Ginzburg and Iain Gordon.
Type A Cheredink algebras H_c, which are particular deformations of the twisted group ring of the nth Weyl algebra by the symmetric group S_n, form an intriguing class of algebras with many interactions with other areas of mathematics. In earlier work with Iain Gordon we used ideas from noncommutative geometry to prove a sort of BeilinsonBernstein equivalence of categories, thereby showing that H_c (or more formally its spherical subalgebra U_c) is a noncommutative deformation of the Hilbert scheme Hilb(n) of n points in the plane.
There is however a second way of relating U_c to Hilbert schemes, which uses the quantum Hamiltonian reduction of Gan and Ginzburg. In the first part of the talk we will show that these two methods are actually equivalent. In the second part of the talk we will use this to prove that the characteristic varieties of irreducible U_cmodules are equidimensional subshemes of Hilb(n), thereby answering a question from the original work with Gordon.


ALTW02 
24th March 2009 14:00 to 15:00 
Algebraic group analogues of the Slodowy slices and deformed Poisson Walgebras
We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g. The new slices are transversal to the conjugacy classes in an algebraic group with Lie algebra g. These slices are associated to the pairs (p,s), where p is a parabolic subalgebra in g and s is an element of the Weyl group W of g. In the algebraic group framework simple Kleinian singularities are realized as the singularities of the fibers of the restriction of the conjugation quotient map to the slices associated to pairs (b,s), where b is a Borel subalgebra in g and s is an element of W whose representative in G is subregular. We also define some Poisson structures on the slices associated to the pairs (p,s). These structures are analogous to the Poisson structures introduced by DeBoer, Tjin and Premet on the Slodowy slices in complex simple Lie algebras. The quantum deformations of these Poisson structures are known as Walgebras of finite type. One of applications of our construction gives rise to new Poisson structures on the coordinate rings of simple Kleinian singularities.


ALTW02 
24th March 2009 15:30 to 16:30 
T Suzuki 
Conformal field theory and Cherednik algebras
I would like to discuss about a physical background of the connection between representaions of Lie, Hecke and Cherednik algebras. For example, I will explain how conformal field theory gives a natural construction of the functors between the category of highest weight representations of the affine Lie algebras and the category of highest weight representations of the rational/trigonometric Cherednik algebras of type A.


ALTW02 
24th March 2009 16:30 to 17:30 
Langlands duality for representations of quantum groups
This is a joint work with E. Frenkel.
We establish a correspondence (or duality) between the characters and the crystal bases of finitedimensional representations of quantum groups associated to Langlands dual semisimple Lie algebras. This duality may also be stated purely in terms of semisimple Lie algebras. To explain this duality, we introduce an "interpolating quantum group" depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.


ALTW02 
25th March 2009 09:00 to 10:00 
Irreducible finite dimensional representations of Walgebras
Walgebras (of finite type) are certain associative algebras constructed from nilpotent orbits in semisimple Lie algebras. In this talk I am going to describe a relation between irreducible finite dimensional representations of a Walgebra and primitive ideals of the universal enveloping algebra whose associated variety coincides with the closure of the given orbit.


ALTW02 
25th March 2009 10:00 to 11:00 
Mickelsson algebras and irreducible representations of Yangians
Yangians and their twisted analogues first appeared as basic examples of deformations of affine Lie algebras, and found numerous applications in Quantum Integrable Systems. Classification of the irreducible finitedimensional representations of Yangians has been known for a long time, but explicit realizations of irreducibles were not known except in special cases. In this talk, we present such a realization. It has basic features of representation theory of reductive groups and uses the theory of Mickelsson algebras as an important technical tool. This a joint work with M.Nazarov.


ALTW02 
25th March 2009 11:30 to 12:30 
Cherednik algebra, CalogeroMoser space and Bethe ansatz
We show that the center of the rational Cherednik algebra is naturally identified with a Bethe algebra of the Gaudin model. At the same time, using the algebraic Bethe ansatz we prove that the Bethe algebra is isomorphic to the space of regular functions on the CalogeroMoser space. We discuss the implications of these constructions.


ALTW02 
26th March 2009 09:00 to 10:00 
V Futorny 
Parabolic induction for Affine KacMoody algebras
We will discuss the category of weight modules with nonzero central charge over affine Lie algebras. Though the classification of irreducible modules with finitedimensional weight spaces in this category is known, it remains open in general. The talk will focus on recent progress in the study of parabolic induction for affine KacMoody algebras which provides a recipe to construct new irreducible modules is the above category. The talk is based on joint results with I.Kashuba.


ALTW02 
26th March 2009 10:00 to 11:00 
M Finkelberg 
Affine GelfandTsetlin bases and affine Laumon spaces
Affine Laumon space P is the moduli space of parabolic sheaves of rank n on the product of 2 projective lines. The natural correspondences give rise to the action of affine Yangian of sl(n) on the equivariant cohomology of P. The resulting module M is isomorphic to the universal Verma module over the affine gl(n). The classes of torus fixed points form a basis of M which is an affine analogue of the classical GelfandTsetlin basis. The Chern classes of tautological vector bundles on P can be computed in terms of the affine Yangian action on M.
This is a joint work with B.Feigin, A.Negut, and L.Rybnikov.


ALTW02 
26th March 2009 11:30 to 12:30 
The impact of Goldie’s theorem on primitive ideal theory In 1958 Alfred Goldie published a seemingly rather abstract theorem stating that many important rings admit a calculation of fractions. This was soon realized to be a deep and fundamental result, particularly leading to a numerical invariant known as Goldie rank. Through Duflo’s theorem one may parameterize the primitive spectrum of an enveloping algebra in the semisimple case by the dual of the Cartan. Then astonishingly, Goldie rank is given through a family of polynomials. Moreover these polynomials have some remarkable properties. For example they form a basis of a multiplicity free representation of the Weyl group. One thereby obtains a quite unattended connection with the Springer theory relating Weyl group representations to the geometry of nilpotent orbits. The polynomials that define Goldie rank are determined up to a scale factor by an explicit formula involving the KazhdanLusztig polynomials and were even a motivation for the precise definition of the latter. These scale factors can be largely determined by finding the locus of Goldie rank one, a problem which has remained open for some thirty years. Another related question is to describe the Goldie rank one sheets (of which there are just finitely many, by virtue of a positivity property of Goldie rank polynomials coming from geometry) and in particular to determine their topology. Combined with the GelfandKirillov conjecture, primitive quotients of enveloping algebras are described (in principle) as matrix rings over differential operators linked to symplectic structure, exactly like Dirac’s relativistic quantum mechanical equation. Thus primitive ideal theory is intimately related to Quantization. In this lecture we review the main results and open problems of the theory. 

ALTW02 
26th March 2009 15:30 to 16:30 
V Kac 
An explicit construction of the complex of variational calculus and Lie conformal algebra cohomology
Lie conformal algebras encode the singular part of the operator product expansion of chiral fields in conformal field theory, and, at the same time, the local Poisson brackets in the theory of soliton equations. That is why they form an essential part of the vertex algebra and Poisson vertex algebra theories. The structure and cohomology theory of Lie conformal algebras was developed about 10 years ago. In a recent joint work with Alberto De Sole we show that the Lie conformal algebra cohomology can be used to explicitly construct the complex of calculus of variations, which is the resolution of the variational derivative map of Euler and Lagrange.


ALTW02 
26th March 2009 16:30 to 17:30 
Poisson vertex algebras in the theory of Hamiltonian equations
We describe the interplay between the theory of Poisson vertex algebras (and, more in general, of conformal algebras) and the theory of Hamiltonian equations and their integrability.


ALTW02 
27th March 2009 09:00 to 10:00 
A Molev 
Higher Sugawara operators and the classical Walgebra for gl n
We give an explicit description of the center of the affine vertex algebra for gl n at the critical level. The results are applied to construct generators of the classical Walgebra for gl n and calculate the eigenvalues of the central elements in the Wakimoto modules at the critical level.


ALTW02 
27th March 2009 10:00 to 11:00 
Nonreductive lie algebras and their representations with good invarianttheoretic properties
One of the main topics of Invariant Theory is to describe finitedimensional representations of complex reductive groups with good properties of algebras of invariants. For instance, it is known that, for simple algebraic groups, most of irreducible representations with polynomial algebras of invariants occur in connection with periodic automorphisms of semisimple Lie algebras. (These are the socalled "$\Theta$groups" of Vinberg.)
In my talk, I will discuss several constructions of nonreductive algebras having polynomial algebras of invariants for the adjoint or coadjoint representations (e.g. contractions of semisimple algebras and iterated semidirect products). Some of these coadjoint representations can also be understood as $\Theta$group associated with periodic automorphisms of nonreductive Lie algebras. There are also possibilities for constructing more general representations with polynomial algebras of invariants using biperiodic gradings and contractions.


ALTW02 
27th March 2009 15:30 to 16:30 
V Serganova 
Geometric induction for algebraic supergroups
Let G be a classical algebraic supergroup, and H be its subgroup. The geometric induction functor is the derived functor from the category of Hmodules to the category of Gmodules. It is defined as the cohomology of vector bundles on G/H. We study this functor in detail in case when H is a parabolic subgroup and G=SL(m,n) or OSP(m,2n) and use this result to find the characters of all irreducible representations of G.


ALTW02 
27th March 2009 16:30 to 17:30 
P Etingof 
Representation theory in complex rank The subject of representation theory in complex rank was started by P.Deligne, who defined complex rank analogs for the classical complex groups GL(N),O(N),and Sp(N), and (later) for the symnmetric group S_N. These are certain symmetric tensor categories of superexponential growth (i.e. nonTannakian), in which the dimension N of the generating object is a generic complex number. Later F.Knop generalized the latter construction to a large class of finite groups (such as general linear groups over a finite field). For generic N, these categories are semisimple, so one may think of these results as "compact" representation theory in complex rank. I will speak about "noncompact" representation theory in complex rank. The discussion will include classical real groups (i.e., classical symmetric pairs), degenerate affine Hecke algebras, rational Cherednik algebras, affine Lie algebras, Yangians, and so on. By definition, a representation of a "noncompact algebra" of complex rank is a representation of its "maximal compact subalgebra" (i.e. an (ind)object of the corresponding tensor category) together with some additional structure (morphisms satisfying some relations). I will discuss the explicit form of such morphisms and relations in several special cases (such as rational Cherednik algebras). This approach leads to a multitude of new interesting representation categories, which, in a sense, capture the phenomenon of "stabilization with respect to rank" in representation theory of classical groups and algebras. 

ALT 
31st March 2009 15:00 to 16:00 
DeligneLusztig varieties and cyclotomic Hecke algebras  
ALT 
2nd April 2009 14:00 to 15:00 
On the number of conjugacy classes of a finite group  
ALT 
2nd April 2009 15:15 to 16:15 
Translations for finite Walgebras  
ALT 
7th April 2009 15:00 to 16:00 
Decomposition matrices and parametrisations of simple modules for Hecke algebras  
ALT 
9th April 2009 15:00 to 16:00 
Lusztig's conjecture via moment graphs  
ALTW03 
13th April 2009 13:00 to 14:00 
Geometry and categorification 1 Categorification via geometric Satake correspondence  
ALTW03 
13th April 2009 14:30 to 15:30 
Representation theory and categorification I Dmodules and localisation  
ALTW03 
13th April 2009 16:00 to 17:00 
Topology and categorification I Introduction to ReshetikhinTurgev invariants and modular categories  
ALTW01 
14th April 2009 09:00 to 10:00 
Geometry and categorification II Braid group actions in algebraic geometry  
ALTW03 
14th April 2009 10:30 to 11:30 
Representation theory and categorification II Hall algebras, quivers, and canonical bases  
ALTW03 
14th April 2009 11:35 to 12:35 
Categorification via Floer homology and the SeidelSmith construction  
ALTW03 
14th April 2009 13:55 to 14:55 
Geometry and categorification II Categorical sl(2) actions on categoris of coherant sheaves  
ALTW03 
14th April 2009 15:00 to 16:00 
Representation theory and categorification III Further examples  
ALTW03 
14th April 2009 16:30 to 17:30 
Topology and categorification III Modular categories and rational conformat field theory  
ALTW03 
15th April 2009 09:30 to 10:30 
The graded LascouxLeclercThibon conjecture
In type A, some new algebras introduced recently by KhovanovLauda and Rouquier give rise to remarkable Zgradings on group algebras of symmetric groups and more generally on various cyclotomic Hecke algebras. There are also graded versions of Specht modules for these algebras. In recent work joint with Kleshchev we have computed the qdecomposition numbers of these graded Specht modules. The result, which gives a graded version of the LascouxLeclercThibon conjecture, is best expressed in the language of categorification.


ALTW03 
15th April 2009 11:00 to 12:00 
Categorification and topology
The relation between ncategories and topology is clarified by a collection of hypotheses, some of which have already been made precise and proved. The "homotopy hypothesis" says that homotopy ntypes are the same as ngroupoids. The "stabilization hypothesis" says that each column in the periodic table of ncategories stabilizes at a certain precise point. The "cobordism hypothesis" gives an ncategorical description of cobordisms, while the "tangle hypothesis" does the same for tangles and their higherdimensional relatives. We shall sketch these ideas, describe recent work by Lurie and Hopkins on the cobordism and tangle hypotheses, and, time permitting, say a bit about how these ideas are related to other lines of work on categorification.


ALTW03 
15th April 2009 13:30 to 14:30 
L Crane 
Categorification and physical spacetime
Categorification was originally invented to solve problems in Mathematical Physics, namely construction of TQFTs and more fundamentally of the quantum theory of gravity. I will discuss the original motivations and more recent developments.


ALTW03 
15th April 2009 14:30 to 15:30 
The periodicity conjecture via 2CalabiYau categories
The periodicity conjecture for pairs of Dynkin diagrams was formulated at the beginning of the nineties in mathematical physics, in work of Zamolodchikov, RavaniniTateoValleriani and KunibaNakanishi. We outline a proof based on the machinery of FominZelevinsky's cluster algebras and their (additive) categorification via 2CalabiYau categories.


ALTW03 
15th April 2009 16:00 to 17:00 
M Khovanov 
Categorification of quantum groups
I'll go over a joint work with Aaron Lauda on categorifications of positive halves of quantum universal enveloping algebras as well as categorification of the BLM form of quantum sl(n).


ALTW03 
16th April 2009 09:30 to 10:30 
Categorifying quantum sl2
Igor Frenkel introduced the idea that the quantum enveloping algebra of sl(2) could be categorified at generic q using its canonical basis. In my talk I will describe a realization of Frenkel's proposal using a diagrammatic calculus.
If time permits I will also explain joint work with Mikhail Khovanov on how this construction can be generalized to quantum sl(n).


ALTW03 
16th April 2009 11:00 to 12:00 
Representation theory of the symmetric group via categorification
The action of projective functors on the regular block of the BGG category O for the Lie algebra sl(n) categorifies the right regular representation of the symmetric group S(n). I will try to describe how one can use representationtheoretic properties of this action to deduce some results about representations of S(n), in particular, about simple modules, induced modules, certain filtrations, and Wedderburn's decomposition of the group algebra.


ALTW03 
16th April 2009 13:30 to 14:30 
Convolutions on lie groups and lie algebras and ribbon 2knots  
ALTW03 
16th April 2009 14:30 to 15:30 
Sutured Floer homology: de (and re) categorification
Sutured Floer homology is an invariant of sutured manifolds introduced by Andras Juhasz. In this talk I'll explain how to first decategorify this invariant to produce an invariant that is much like the Alexander polynomial; and then recategorify to give a definition of sutured Floer homology related to the bordered Floer homology of Lipshitz, Ozsvath and Thurston. This is joint work with Andras Juhasz and Stefan Friedl.


ALTW03 
16th April 2009 16:00 to 17:00 
Higher representation theory
We have introduced a 2category associated with a KacMoody algebra (the type A case goes back to joint work with Joe Chuang and a close version of the positive half has been introduced independently by Khovanov and Lauda). We will discuss the 2representation theory, ie, actions of this 2category on categories (additive, abelian, triangulated, dg...). We will present a unicity result for simple integrable 2representations and JordanHolder series. We will explain the realisation of simple 2representations as categories of sheaves on quiver varieties and deduce the description of classes of indecomposable projective modules as canonical basis elements.


ALTW03 
17th April 2009 09:30 to 10:30 
R Thomas 
Joyce's Hall algebra
I appear to be at the wrong conference, but I do know that some representation theorists like RingelHall algebras, so I’ll describe a bit of Joyce’s stacky Hall algebra and how one can use it.


ALTW03 
17th April 2009 11:00 to 12:00 
Higher dimensional cobordism categories and their topology
Cobordism categories are at the foundations of topological quantum field theory. We will discuss how to define a strict higher dimensional version of the cobordism category, associate a topological space to them, and explain how these spaces relate to classical spaces in cobordism theory as studied by Thom and others in the middle of the last century.


ALTW03 
17th April 2009 14:30 to 15:10 
Categorical geometric skew Howe duality
I will explain a construction of the categorification of the braiding for tensor products of minuscule representations of sl(n). Our construction uses skew Howe duality and the machinery of categorical sl(2) actions. This is joint work with Sabin Cautis and Anthony Licata.


ALTW03 
17th April 2009 15:10 to 15:50 
Symplectic instanton homology
Floer's instanton homology was originally defined as an invariant of integral homology 3spheres. The AtiyahFloer Conjecture claims that there should be a symplectic counterpart to instanton theory, based on Lagrangian Floer homology. Starting from a Heegaard decomposition of a 3manifold, I will explain one way to make sense of the symplectic side of the AtiyahFloer conjecture, for arbitrary 3manifolds. This is joint work with Chris Woodward.


ALTW01 
17th April 2009 16:20 to 17:00 
Integral lattices in TQFT and integral modular categories
The SO(3)TQFT at an odd prime has a natural integral structure. It means that all matrix coefficients of the mapping class group representations in this theory are algebraic integers. I will discuss the structure of the resulting "integral modular functor". This is joint work with Patrick Gilmer.


ALTW03 
18th April 2009 09:30 to 10:30 
Categorifying integral polytops geometry
The subjcet of combinatorics of integer polytopes is known to be related to geometry of toric varieties. Recently, this relation has received a categorical interpretation as an equivalence of derived categories. We will discuss this equivalence and related results.


ALTW03 
18th April 2009 10:30 to 11:00 
Uhlenbeck compactifications as a stack
I will explain how the Uhlenbeck compactification of vector bundles on a smooth projective surface can be defined as a functor of families (i.e. as an algebraic stack). I will also explain how Hecke correspondences which modify a vector bundle along a divisor on a surface, can be extended to the Uhlenbeck compactification. This construction is related to the conjectural higher dimensional Geometric Langlands program


ALTW03 
18th April 2009 12:00 to 13:00 
Threedimensional topological field theory anda categorification of the derived category of coherent sheaves
The RozanskyWitten model is a 3d topological sigmamodel whose target space X is a complex symplectic manifold. I will describe the 2category structure on the set of its boundary conditions and show that it is a categorification of the derived category of coherent sheaves on X. In the special case when X is a cotangent bundle to a complex manifold Y, this 2category is closely related to the 2category of derived categorical sheaves over Y introduced by Toen and Vezzosi. I will also explain a surprising connection between a categorification of deformation quantization and complex symplectic geometry.


ALT 
21st April 2009 15:00 to 16:00 
T Burness  Permutation groups, derangements and prime order elements  
ALT 
23rd April 2009 14:00 to 15:00 
Lsmall representations of a reductive group  
ALT 
23rd April 2009 15:15 to 16:15 
Some recent observations on generalised Schur algebras  
ALT 
28th April 2009 14:00 to 15:00 
D Juteau  Cohomology of the minimal nilpotent orbit  
ALT 
28th April 2009 15:15 to 16:15 
Towards a padic Langlands correspondence: construction of (phi, Gamma)modules  
ALT 
30th April 2009 14:00 to 15:00 
KazhdanLusztig cells in affine Weyl groups  
ALT 
30th April 2009 15:15 to 16:15 
MV polytopes and components of quiver varieties  
ALT 
5th May 2009 10:00 to 12:00 
Trying to construct explicitly kernels for Langlands' functoriality 1 I want to explain part of my present research work on Langlands' functoriality principle. The validity of Langlands' transfer of automorphic representations from an arbitrary reductive group G to a linear group GL(r) is equivalent to the existence of a huge family of "kernel functions" on the product of the adelic groups associated to G and GL(r). The purpose of these lectures is to propose explicit formulas for these kernel functions (in the everywhere unramified case over function fields F, for the sake of simplicity, even though it could be done as well in the case of number fields, with some extra work at archimidean places). It can be done by combining explicit local constructions and summations over some discrete groups of rational points. These constructions only make use of function theory on local groups. They can be phrased without any use of global automorphic representations theory. Langlands' functoriality principle is equivalent to the fact that these explicit kernel functions are left invariant by the discrete arithmetic group GL(r,F). 

ALT 
5th May 2009 15:00 to 16:00 
E Letellier  Topology of quiver varieties and the character ring of finite general linear groups  
ALT 
7th May 2009 14:00 to 15:00 
G Williamson  Some geometric constructions of link homology  
ALT 
7th May 2009 15:15 to 16:15 
Quiver presentations of descent algebras of finite Coxeter groups  
ALT 
11th May 2009 17:00 to 18:00 
L Lafforgue 
RVP lecture: Langlands' functoriality viewed as a kind of function theoretic Poisson formula problem
Langlands' functoriality conjecture is one of the most important problems in automorphic representations theory.
In the case of transfer of unramified representations between linear groups, we give an equivalent formulation of this conjecture which looks like a Poisson formula :
two linear functionnals defined on some huge space of functions on adelic groups have to be equal.
These two liear functionnals are defined by some local constructions (on groups over the local completions of the global field) followed by summation over some groups of rational points.


ALT 
12th May 2009 10:00 to 12:00 
Trying to construct explicitly kernels for Langlands' functoriality 2 I want to explain part of my present research work on Langlands' functoriality principle. The validity of Langlands' transfer of automorphic representations from an arbitrary reductive group G to a linear group GL(r) is equivalent to the existence of a huge family of "kernel functions" on the product of the adelic groups associated to G and GL(r). The purpose of these lectures is to propose explicit formulas for these kernel functions (in the everywhere unramified case over function fields F, for the sake of simplicity, even though it could be done as well in the case of number fields, with some extra work at archimidean places). It can be done by combining explicit local constructions and summations over some discrete groups of rational points. These constructions only make use of function theory on local groups. They can be phrased without any use of global automorphic representations theory. Langlands' functoriality principle is equivalent to the fact that these explicit kernel functions are left invariant by the discrete arithmetic group GL(r,F). 

ALTW05 
13th May 2009 11:00 to 12:00 
J Coates  Lfunctions and arithmetic  
ALTW05 
13th May 2009 13:45 to 14:45 
What is an algebraic automorphic form?  
ALTW05 
13th May 2009 15:15 to 16:15 
M Rapoport  Arithmetic cycles on moduli spaces of abelian varieties  
ALTW05 
13th May 2009 16:30 to 17:30 
G Laumon  Fundamental lemma and Hitchin fibration  
ALT 
14th May 2009 14:00 to 15:00 
Refinements of the Bruhat decomposition and structure constants of Hecke algebras of finite Chevally groups  
ALT 
14th May 2009 15:15 to 16:15 
A Zelevinsky  Cluster algebras via quivers with potentials  
ALT 
19th May 2009 10:00 to 12:00 
Trying to construct explicitly kernels for Langlands' functoriality 3 I want to explain part of my present research work on Langlands' functoriality principle. The validity of Langlands' transfer of automorphic representations from an arbitrary reductive group G to a linear group GL(r) is equivalent to the existence of a huge family of "kernel functions" on the product of the adelic groups associated to G and GL(r). The purpose of these lectures is to propose explicit formulas for these kernel functions (in the everywhere unramified case over function fields F, for the sake of simplicity, even though it could be done as well in the case of number fields, with some extra work at archimidean places). It can be done by combining explicit local constructions and summations over some discrete groups of rational points. These constructions only make use of function theory on local groups. They can be phrased without any use of global automorphic representations theory. Langlands' functoriality principle is equivalent to the fact that these explicit kernel functions are left invariant by the discrete arithmetic group GL(r,F). 

ALT 
19th May 2009 15:15 to 16:15 
C De Concini  Quotients of symmetric varieties  
ALT 
19th May 2009 16:30 to 17:30 
From splines to the index theorem  
ALT 
21st May 2009 14:00 to 15:00 
Types for padic classical groups  
ALT 
21st May 2009 15:15 to 16:15 
An algebraic slice in the coadjoint action of the Borel  
ALT 
26th May 2009 10:00 to 12:00 
Trying to construct explicitly kernels for Langlands' functoriality 4 I want to explain part of my present research work on Langlands' functoriality principle. The validity of Langlands' transfer of automorphic representations from an arbitrary reductive group G to a linear group GL(r) is equivalent to the existence of a huge family of "kernel functions" on the product of the adelic groups associated to G and GL(r). The purpose of these lectures is to propose explicit formulas for these kernel functions (in the everywhere unramified case over function fields F, for the sake of simplicity, even though it could be done as well in the case of number fields, with some extra work at archimidean places). It can be done by combining explicit local constructions and summations over some discrete groups of rational points. These constructions only make use of function theory on local groups. They can be phrased without any use of global automorphic representations theory. Langlands' functoriality principle is equivalent to the fact that these explicit kernel functions are left invariant by the discrete arithmetic group GL(r,F). 

ALT 
26th May 2009 15:00 to 16:00 
Two partially ordered sets arising from nilpotent orbits  
ALTW06 
27th May 2009 11:10 to 12:10 
M Aschbacher  Ngroups, 3' groups and fusion systems  
ALTW06 
27th May 2009 14:00 to 15:00 
D Segal  CFSG and group theory  
ALTW06 
27th May 2009 15:15 to 16:15 
Is the nondiscrete side of locally compact groups more tractable?  
ALTW06 
27th May 2009 17:00 to 18:00 
Braid groups and representations of symmetric groups  
ALTW06 
28th May 2009 09:30 to 10:30 
I Capdeboscq  Finite simple groups of "medium size"  
ALTW06 
28th May 2009 11:00 to 12:00 
Element orders and Sylow structure  
ALTW06 
28th May 2009 14:00 to 15:00 
M Liebeck  Density of character degrees  
ALTW06 
28th May 2009 15:15 to 16:15 
The quaquaversal group  
ALTW06 
28th May 2009 17:00 to 18:00 
R Guralnick  Permutation groups and coverings of curves  
ALTW06 
29th May 2009 09:30 to 10:30 
PH Tiep  Brauer height zero conjecture for 2blocks of maximal defect  
ALTW06 
29th May 2009 11:00 to 12:00 
An action of SL(2,Z) on the space of Dirichlet series, and some associated computations  
ALTW06 
29th May 2009 12:00 to 13:00 
Pseudo reductive groups over GF(x)  
ALT 
4th June 2009 14:00 to 15:00 
HH Andersen  Rigidity of tilting modules  
ALT 
4th June 2009 15:15 to 16:15 
Quantum cohomology of the Springer resolution and affine KZ connections  
ALT 
9th June 2009 15:00 to 16:00 
Total positivity for loop groups  
ALT 
16th June 2009 14:00 to 15:00 
Geometry of the exotic nilpotent cone  
ALT 
16th June 2009 15:15 to 16:15 
CarterPayne homomorphisms for Hecke algebras
In a famous paper Carter and Payne, building on work of Carter and Lusztig, constructed a family of homomorphisms between different Specht modules and Weyl modules of the symmetric and general linear groups, respectively. In a few special cases these maps have been generalised to give corresponding maps between the qanalogues of the Specht modules and Weyl modules, however, the full qanalogue of CarterPayne remains open. In this talk I will describe an qanalogue of the CarterPayne maps which are indexed by partitions with "large gaps". If time permits I will also describe how to lift CarterPayne maps to the graded setting.
This is joint work with Sinead Lyle.


ALT 
18th June 2009 15:00 to 16:00 
Chiral differential operators on flag manifolds and KacMoody algebras at the critical level  
ALTW04 
22nd June 2009 10:00 to 11:00 
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.


ALTW04 
22nd June 2009 11:30 to 12:30 
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 HarishChandra \mufunctions 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 padic 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 IwahoriMatsumoto 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). 

ALTW04 
22nd June 2009 14:00 to 15:00 
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 Gequivariant 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 ladic perverse sheaves. In particular, this category is quasihereditary and admits a mixed structure. If time permits, I will describe some small examples. Some of these results are joint work with David Treumann.


ALTW04 
22nd June 2009 15:30 to 16:30 
V ToledanoLaredo 
Stability conditions and Stokes factors
I will explain how the wallcrossing 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 RingelHall 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.


ALTW04 
22nd June 2009 16:30 to 17:30 
Higher representations: geometry and tensor structures
We will discuss the geometrical realisation of simple 2representations of symmetric KacMoody algebras and their tensor products on one hand, and the algebraic construction of tensor products on the other hand.


ALTW04 
23rd June 2009 09:00 to 10:00 
Graded qSchur algebras
Just 10 years ago, the decomposition matrix theorem for cyclotomic Hecke algebras was generalized to the decomposition matrix theorem for the qSchur 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 qSchur algebra. This may be done by defining appropriate setting for the graded version, and following ideas of Hemmer and Nakano, and Leclerc.


ALTW04 
23rd June 2009 10:00 to 11:00 
E Friedlander 
Investigating $kG$modules using nilpotent operators
This is a report of ongoing 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 1parameter 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.


ALTW04 
23rd June 2009 11:30 to 12:30 
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 BradenMacPherson 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.


ALTW04 
23rd June 2009 14:00 to 15:00 
D Nakano 
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 selfinjective 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.


ALTW04 
23rd June 2009 15:30 to 16:30 
On CasselmanWallach 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.


ALTW04 
24th June 2009 09:00 to 10:00 
RM Guralnick 
Derangements in Finite and Algebraic Groups
A derangement is a fixed point free permutation. We will consider transitive actions of finite and algebraic groups and the prevalence of derangements. We will discuss the BostonShalev conjecture and related problems about conjugacy classes as well as various applications.


ALTW04 
24th June 2009 10:00 to 11:00 
Quadratic unipotent blocks of finite general linear, unitary and symplectic groups
Let G be a finite reductive group. The (complex) irreducible characters of G were classified by Lusztig. They fall into Lusztig series E(G, (s)) where (s) is a semisimple class in a dual group G*. If a character is in E(G, (1)) it is a unipotent character. Let l be a prime different from the characteristic of the field of definition of G. A block of lmodular characters containing unipotent characters is a unipotent block.
Unipotent blocks of finite reductive groups have been intensely investigated by many authors over many years. In particular, correspondences such as perfect isometries (in the sense of Michel Broue) or derived equivalences have been established between unipotent blocks of two general linear groups, a finite reductive group and a "local" subgroup, and so on.
In this talk we will focus on recent work which shows that if we enlarge the set of unipotent blocks to the set of "quadratic unipotent blocks" for some choices of l some surprising results "across types" are obtained. In particular, correspondences are obtained between blocks of a unitary group and a symplectic group, and between blocks of a general linear group and a symplectic group. It would appear that quadratic unipotent blocks are a natural generalization of unipotent blocks in classical groups.


ALTW04 
24th June 2009 11:30 to 12:30 
D Juteau 
Perverse sheaves and modular representation theory
I will talk about some relationships between modular representation theory and perverse sheaves with positive characteristic coefficients.


ALTW04 
25th June 2009 09:00 to 10:00 
A Premet 
Modular Lie algebras and the GelfandKirillov conjecture
In my talk I am going to discuss the current status of the GelfandKirillov conjecture (from 1966) on the structure of the Lie field of a finite dimensional complex simple Lie algebra


ALTW04 
25th June 2009 10:00 to 11:00 
Noncommutative invariant theory
We define a (noncommutative) quantum analogue of the coordinate ring of a finite dimensional module of a quantum group, which in many (but not all) cases is a flat deformation of the classical coordinate ring. We prove a quantum analogue of the first fundamental theorem of invariant theory in a form which generalises the classical cases. This is joint work with R. Zhang and H. Zhang.


ALTW04 
25th June 2009 11:30 to 12:30 
Canonical bases and KLRalgebras
We'll explain how KhovanovLaudaAlgebras categorify the canonical basis of the negative part of the quantum enveloping algebra, and we'll give some motivation for such constructions which come from Cherednik algebras.


ALTW04 
25th June 2009 14:00 to 15:00 
Total positivity, Schubert positivity, and geometric Satake
Let G be a complex simple simplyconnected algebraic group. A theorem proved independently by Ginzburg and Peterson states that the homology H_*(Gr_G) of the affine Grassmannian of G is isomorphic to the ring of functions on the centralizer X of a principal nilpotent in the Langlands dual G^\vee. There is a notion of total positivity on X, using Lusztig's general definitions, and there is also a notion of Schubert positivity, using Schubert classes of Gr_G. We connect the two notions using the geometric Satake correspondence. In addition, we give an explicit parametrization of the positive points of X.
This is joint work with Konstanze Rietsch, generalizing work of hers in type A.


ALTW04 
25th June 2009 15:30 to 16:30 
I Cherednik 
Difference spherical and Whittaker functions
The definition of q,tspherical functions was sugested by the speaker (reduced root systems) and Stokman (the CcheckC case). They generalize the classical spherical functions, the basic hypergeometric function and the padic spherical functions. Recently, their systematic algebraic and analytic theory was started including qgeneralizations of the HarishChandra asymtotic formula and the HelgasonJohnson description of bounded spherical functions, as well as the theory of the qWhittaker functions. The latter are related to the GiventalLee theory, the ICtheory of the affine flag varieties and are expected to have connections with the quantum geometric Langlands program.


ALTW04 
26th June 2009 09:00 to 10:00 
W Soergel 
Graded version of tensoring with finite dimensional representations
I want to discuss how to lift the functors of tensoring with a finite dimensional representation to the graded representation categories and what these functors correspond to under Koszul duality


ALTW04 
26th June 2009 10:00 to 11:00 
On classification of Poisson vertex algebras  
ALTW04 
26th June 2009 11:30 to 12:30 
Onedimensional representations of Walgebras
Premet conjectured that any (finite) Walgebra has a onedimensional representation. The goal of this talk is to explain results of the speaker towards this conjecture. We will start giving a sketch of proof for the classical Lie algebras. Then we explain a reduction to rigid nilpotent elements using a parabolic induction functor. Finally, we will explain how using the BrundanGoodwinKleshchev category O one can try to describe onedimensional representations of Walgebras associated to rigid elements in exceptional Lie algebras.


ALTW04 
26th June 2009 14:00 to 15:00 
Compactification of DeligneLusztig varieties
Joint work with Raphaël Rouquier: we give an explicit construction of the normalization of the BottSamelsonDemazure compactification of DeligneLusztig varieties in their classical étale covering (with a finite torus as Galois group). We retrieve an old result of Deligne and Lusztig about the local monodromy around the divisors of this compactification.


ALTW04 
26th June 2009 15:30 to 16:30 
DeligneLusztig varieties, Braid groups and cyclotomic Hecke algebras  
ALTW07 
12th September 2011 10:00 to 11:00 
Koszulity of the walled Brauer algebra  
ALTW07 
12th September 2011 11:30 to 12:30 
T Tanisaki  Differential operators on quantized flag manifolds  
ALTW07 
12th September 2011 14:00 to 15:00 
D Rumynin  Double Cells and Representations  
ALTW07 
12th September 2011 15:30 to 16:30 
Categorification, canonical bases and knot invariants  
ALTW07 
13th September 2011 09:00 to 10:00 
Quasiisolated blocks of exceptional groups  
ALTW07 
13th September 2011 10:00 to 11:00 
G Williamson  Some applications of parity sheaves  
ALTW07 
13th September 2011 14:00 to 15:00 
Some remarks on endomorphism rings and realizability questions  
ALTW07 
13th September 2011 15:30 to 16:30 
Lie powers for general linear groups and Lie modules for symmetric groups  
ALTW07 
14th September 2011 09:00 to 10:00 
E Opdam  Extensions of tempered representations and Rgroups  
ALTW07 
14th September 2011 10:00 to 11:00 
W Soergel  Koszul duality in positive characteristic  
ALTW07 
14th September 2011 11:30 to 12:30 
A Premet  Hesselink stratification of nullcones and base change  
ALTW07 
14th September 2011 14:00 to 15:00 
On disconnected reductive groups  
ALTW07 
15th September 2011 09:00 to 10:00 
Representations of finite Walgebras associated to classical Lie algebras  
ALTW07 
15th September 2011 10:00 to 11:00 
Perverse sheaves on affine Grassmanians and geometry of the dual group  
ALTW07 
15th September 2011 11:30 to 12:30 
T Arakawa  Localization of affine Walgebras at the critical level  
ALTW07 
15th September 2011 14:00 to 15:00 
On critical level representations of affine KacMoody algebras  
ALTW07 
16th September 2011 09:00 to 10:00 
The Odd NilHecke algebra  
ALTW07 
16th September 2011 10:00 to 11:00 
Categorification and finite dimensional modules of DAHA  
ALTW07 
16th September 2011 11:30 to 12:30 
D Juteau  Singularities in nilpotent cones of exceptional type  
ALTW07 
16th September 2011 14:00 to 15:00 
Elliptic Schubert calculus 