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Book DetailsContemporary MathematicsVolume: 691; 2017; 376 ppMSC: Primary 20; 22; 11; 19
This volume contains the proceedings of the international conference “Around Langlands Correspondences”, held from June 17–20, 2015, at Université 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 BaumConnes 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.
ReadershipGraduate students and research mathematicians interested in automorphic forms, representation theory, and the Langlands program.

Table of Contents

Articles

Noriyuki Abe — Change of weight theorem for pro$p$Iwahori Hecke algebras

AnneMarie Aubert, Paul Baum, Roger Plymen and Maarten Solleveld — Conjectures about $p$adic groups and their noncommutative geometry

Indira Chatterji — Introduction to the Rapid Decay property

Tyrone Crisp and Nigel Higson — A second adjoint theorem for ${SL(2,\mathbb {R})}$

JeanFrançois Dat — A functoriality principle for blocks of $p$adic linear groups

Agnès David — Poids de Serre dans la conjecture de Breuil–Mézard

Naoki Imai and Takahiro Tsushima — Affinoids in LubinTate surfaces with exponential full level two

Jie Lin — An automorphic variant of a conjecture of Deligne

Colette Moeglin and David Renard — Paquets d’Arthur des groupes classiques complexes

Ahmed Moussaoui — Proof of the AubertBaumPlymenSolleveld conjecture for split classical groups

Enno Nagel — From crystalline to unitary representations

Alexander Stasinski — Representations of $\mathrm {GL}_N$ over finite local principal ideal rings: An overview

Julianna Tymoczko — The geometry and combinatorics of Springer fibers


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This volume contains the proceedings of the international conference “Around Langlands Correspondences”, held from June 17–20, 2015, at Université 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 BaumConnes 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.
Graduate students and research mathematicians interested in automorphic forms, representation theory, and the Langlands program.

Articles

Noriyuki Abe — Change of weight theorem for pro$p$Iwahori Hecke algebras

AnneMarie Aubert, Paul Baum, Roger Plymen and Maarten Solleveld — Conjectures about $p$adic groups and their noncommutative geometry

Indira Chatterji — Introduction to the Rapid Decay property

Tyrone Crisp and Nigel Higson — A second adjoint theorem for ${SL(2,\mathbb {R})}$

JeanFrançois Dat — A functoriality principle for blocks of $p$adic linear groups

Agnès David — Poids de Serre dans la conjecture de Breuil–Mézard

Naoki Imai and Takahiro Tsushima — Affinoids in LubinTate surfaces with exponential full level two

Jie Lin — An automorphic variant of a conjecture of Deligne

Colette Moeglin and David Renard — Paquets d’Arthur des groupes classiques complexes

Ahmed Moussaoui — Proof of the AubertBaumPlymenSolleveld conjecture for split classical groups

Enno Nagel — From crystalline to unitary representations

Alexander Stasinski — Representations of $\mathrm {GL}_N$ over finite local principal ideal rings: An overview

Julianna Tymoczko — The geometry and combinatorics of Springer fibers