Instructional workshop
Monday 12th January 2009 to Friday 23rd January 2009
08:30 to 10:00  Registration  
10:00 to 11:00 
P Achar ([Louisiana]) 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.)

INI 1  
11:00 to 11:30  Coffee  
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.

INI 1  
12:30 to 13:30  Lunch  
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).

INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
17:30 to 18:30  Wine Reception  
18:45 to 19:30  Dinner 
09:00 to 10:00  Symmetry, polynomials and quantisation  INI 1  
10:00 to 11:00 
P Achar ([Louisiana]) 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.)

INI 1  
11:00 to 11:30  Coffee  
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.

INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
A Kleshchev ([Oregon]) 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.

INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00  Symmetry, polynomials and quantisation  INI 1  
10:00 to 11:00 
P Achar ([Louisiana]) Derived categories and perverse sheaves 
INI 1  
11:00 to 11:30  Coffee  
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.

INI 1  
12:30 to 13:30  Lunch  
18:45 to 19:30  Dinner 
09:00 to 10:00  Symmetry, polynomials and quantisation  INI 1  
10:00 to 11:00 
P Achar ([Louisiana]) Derived categories and perverse sheaves 
INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Categorification of sl(2)modules  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
A Kleshchev ([Oregon]) 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.

INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00  Symmetry, polynomials and quantisation  INI 1  
10:00 to 11:00 
P Achar ([Louisiana]) Derived categories and perverse sheaves 
INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Categorification of sl(2)modules  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
A Kleshchev ([Oregon]) 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.


15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00 
M Broué ([Paris]) Complex reflection groups and their associated braid groups and Hecke algebras 
INI 1  
10:00 to 11:00  Introduction to KazhdanLusztig theory with unequal parameters  INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Higher representations of Lie algebras  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
D Vogan ([Massachusetts]) Schubert varieties and representations of real reductive groups 
INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00 
M Broué ([Paris]) Complex reflection groups and their associated braid groups and Hecke algebras 
INI 1  
10:00 to 11:00  Introduction to KazhdanLusztig theory with unequal parameters  INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Higher representations of Lie algebras  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
D Vogan ([Massachusetts]) Schubert varieties and representations of real reductive groups 
INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00 
M Broué ([Paris]) Complex reflection groups and their associated braid groups and Hecke algebras 
INI 1  
10:00 to 11:00 
I Losev ([Massachusetts]) 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. 
INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Higher representations of Lie algebras  INI 1  
12:30 to 13:30  Lunch  
18:45 to 19:30  Dinner 
09:00 to 10:00 
I Losev ([Massachusetts]) 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. 
INI 1  
10:00 to 11:00  Introduction to KazhdanLusztig theory with unequal parameters  INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Higher representations of Lie algebras  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
D Vogan ([Massachusetts]) Schubert varieties and representations of real reductive groups 
INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00 
I Losev ([Massachusetts]) 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. 
INI 1  
10:00 to 11:00  Introduction to KazhdanLusztig theory with unequal parameters  INI 1  
11:00 to 11:30  Coffee  
11:30 to 12:30  Higher representations of Lie algebras  INI 1  
12:30 to 13:30  Lunch  
14:00 to 15:00 
D Vogan ([Massachusetts]) Schubert varieties and representations of real reductive groups 
INI 1  
15:00 to 15:30  Tea  
15:30 to 16:30  Discussion  INI 1  
16:30 to 17:30  Discussion  INI 1  
18:45 to 19:30  Dinner 
09:00 to 10:00  Geometry and categorification II Braid group actions in algebraic geometry 
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.
