This volume contains the proceedings of the international conference ``Around Langlands Correspondences'', held from June 17-20, 2015, at Universite Paris Sud in Orsay, France.
The Langlands correspondence (nowadays called the usual Langlands correspondence), conjectured by Robert Langlands in the late 1960s and early 1970s, has recently seen some new mysterious generalizations: the modular Langlands correspondence, the $p$-adic Langlands correspondence, and the geometric Langlands correspondence, the last of which seems to share deep connections with the Baum-Connes conjecture.
The aim of this volume is to present, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
N. Abe, Change of weight theorem for pro-$p$-Iwahori Hecke algebras
A.-M. Aubert, P. Baum, R. Plymen, and M. Solleveld, Conjectures about
$p$-adic groups and their noncommutative geometry
I. Chatterji, Introduction to the Rapid Decay property
T. Crisp and N. Higson, A second adjoint theorem for
$\textrm{SL}(2,\mathbb{R})$
J.-F. Dat, A functoriality principle for blocks of $p$-adic linear groups
A. David, Poids de Serre dans la conjecture de Breuil-Mezard
N. Imai and T. Tsushima, Affinoids in Lubin-Tate surfaces with exponential
full level two
J. Lin, An automorphic variant of the Deligne conjecture
C. Moeglin and D. Renard, Paquets d'Arthur des groupes classiques complexes
A. Moussaoui, Proof of the Aubert-Baum-Plymen-Solleveld conjecture for split
classical groups
E. Nagel, From crystalline to unitary representations
A. Stasinski, Representations of $\textrm{GL}_N$ over finite local principal
ideal rings: An overview
J. Tymoczko, The geometry and combinatorics of Springer fibers.
Farrell Brumley, Universite Paris 13, Villetaneuse, France.
Maria Paula Gomez Aparicio, Universite Paris-Sud 11, Orsay, France.
Alberto Minguez, Universite Pierre et Marie Curie, Paris, France.
