Jean-Francois Dat will speak on

Functoriality of local functoriality

Abstract: Langlands duality conjecture predicts that the smooth irreducible representations of a p-adic reductive group G(F) are (almost) parametrized by certain morphisms from the Weil group W_F to the "Langlands dual" group of G. From this conjecture follows "Langlands functoriality principle", which says that, given two groups G,G' over F, any morphism between their dual groups should induce a transfer of (packets of) irreducible representations from G(F) to G'(F). A natural question is : can such a transfer be extended to non-irreducible representations in a functorial way, or even to mod l and l-adic integral representations ? I will advertise a general conjecture that allows to transfer "blocks" of representations, and provide several examples of this phenomenon.