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Abstracts:

Guy Henniart, Université Paris-Sud - "A Satake isomorphism for mod. p representations of reductive groups over local fields" (Joint work with Vignéras)

Abstract: Using congruences of modular forms has had tremendous impact in Number Theory. A natural general framework is the study of congruences between automorphic forms or representations. The local counterpart of that is the study of representations of local reductive groups on vector spaces over finite fields. Here F is a local field with finite residue field of characteristic p, G is a connected reductive group over F and B is a minimal parabolic subgroup of G with Levi decomposition B=LU. Let K be a special parahoric subgroup of G, in good position with respect to (L, U). For any absolutely irreducible smooth representation of K on a vector space V over a field C of characteristic p, we describe the intertwining algebra H(G,K, V) of V in G. More precisely, we define a natural algebra homomorphism from H(G,K,V) to a similar algebra for L, we show it is injective and determine its image. We thus generalise work of Herzig. Contrary to the cases of Herzig, and the classical case, due to Satake, where V is trivial and C is a field of complex numbers, we show that the intertwining algebra H(G, K, V) need not be commutative.

Werner Hoffmann, Universität Bielefeld - "Fourier transforms of weighted orbital integrals on Sp(2,R)"

Abstract: We will present explicit formulas for the Fourier transforms of weighted orbital integrals on the real symplectic group of rank 2. We will also report on partial results for groups of higher rank. Possible applications include Weyl asymptotics for the cuspidal spectrum of arithmetic quotients.

Dipendra Prasad, Tata Institute of Fundamental Research, Mumbai - "Application of base change to certain branching laws for unitary groups for depth zero supercuspidals of DeBacker-Reeder"

Abstract: DeBacker and Reeder have constructed certain L-packet of representations of depth zero to which conjectures with Wee Teck Gan and B. Gross could be put to test. A nice application of base change methods achieves the verification of the conjectures in these cases.

Allan Silberger, Cleveland State University, Ohio - "Level Zero Jacquet-Langlands: Joint Work with Wilhelm Zink, a Historical View

Abstract: I shall review the development of ideas leading to the papers on "explicit matching".

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