## 6 juin 2017

Tasho Kaletha (University of Michigan )
Regular supercuspidal representations

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Lieu : Bât 425, Salle 117-119

Résumé : This talk will concern the representations of reductive groups over local fields. These occur as local components of automorphic representations and this is one motivation for their study. Harish-Chandra has given a simple and explicit classification of the discrete series representations of reductive groups over the real numbers. We will describe a very similar classification that holds for a large proportion of the supercuspidal representations of reductive groups over non-archimedean local fields (which we may call regular). The analogy runs deeper : there is a remarkable parallel between the characters of regular supercuspidal representations and the characters of discrete series representations of real reductive groups. This leads to an explicit construction of the local Langlands correspondence for regular supercuspidal representations. Time permitting, we will touch upon the extension of these methods beyond the regular case.

Marc Levine (Universität Duisburg-Essen)
Résumé : Using methods of motivic stable homotopy theory and the Chow-Witt groups, one can start to give invariants with values in quadratic forms that refine some of the common numerical invariants in algebraic geometry. This includes quadratic refinements of things like Euler charactaristics and degrees of Chern classes. We will give some details on these constructions and indicate how the six-functor formalism allows one to refine the foundations of modern enumerative geometry, specifically, the construction of the virtual fundamental class associated to a perfect obstruction theory, to refined classes in any cohomology theory of motivic type’’.