Speaker: Chuang, Joseph (City University London)
Title: Derived categories and perverse equivalences
Abstract: These lectures will be an introduction to derived categories and derived equivalences in the context of the representation theory of finite groups. Perverse equivalences, certain special derived equivalences that Raphael Rouquier and I have studied, will be featured. Many examples will be discussed, including symmetric groups and finite groups of Lie type.

Speaker: Juteau, Daniel (Université de Caen)
Title: Springer correspondences
Abstract: In 1976 Springer defined a correspondence making a link between the geometry of the nilpotent cone of a reductive Lie algebra and representations of its Weyl group. The correspondence was later reinterpreted in terms of perverse sheaves on the nilpotent cone. It was in some way incomplete: not all simple perverse sheaves appeared. This led Lusztig to define a generalized Springer correspondence in 1984. This construction involved induction and restriction functors between perverse sheaves, from and to Levi subalgebras. The original Springer correspondence corresponds to the case of a maximal torus. In 2007, I defined and studied a modular Springer correspondence, using sheaves and representations in characteristic > 0. Between 2013 and 2015, P. Achar, A. Henderson, S. Riche and I studied the generalized modular case. Since the generalized Springer correspondence played a crucial role in the theory of character sheaves, which was designed to compute character values of finite reductive groups, we hope that the modular version of the story will be useful in their modular representation theory.

<Plan>
1. Springer correspondence
2. Generalized Springer correspondence
3. Modular Springer correspondence
4. Modular Generalized Springer correspondence

Speaker: Letellier, Emmanuel (University of Paris 7)
Title: Fourier transforms in the representation theory of reductive groups over finite fields
Abstract: In these series of lectures I will first recall the motivation of introducing classical Fourier transforms in the representation theory of reductive groups over finite fields and explain how it can be used to slove new problems (like the decomposition of tensor products of irreducibles). In the second part I will discuss exotic Fourier transforms and the connection with Langlands functoriality principle. The second part is a joint project with G. Laumon.