Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms
Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms

Author: Volker Heiermann

Publisher: Springer

Published: 2018-10-01

Total Pages: 367

ISBN-13: 3319952315

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This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.

The Abel Prize 2018-2022
The Abel Prize 2018-2022

Author: Helge Holden

Publisher: Springer Nature

Published: 2024

Total Pages: 876

ISBN-13: 3031339738

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The book presents the winners of the Abel Prize in mathematics for the period 2018-2022: - Robert P. Langlands (2018) - Karen K. Uhlenbeck (2019) - Hillel Furstenberg and Gregory Margulis (2020) - Lászlo Lóvász and Avi Wigderson (2021) - Dennis P. Sullivan (2022) The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos from the period 2018-2022 showing many of the additional activities connected with the Abel Prize. This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer, 2014) as well as on The Abel Prize 2013-2017 (Springer, 2019), which profile the previous Abel Prize laureates.

Zeta Integrals, Schwartz Spaces and Local Functional Equations
Zeta Integrals, Schwartz Spaces and Local Functional Equations

Author: Wen-Wei Li

Publisher: Springer

Published: 2018-11-02

Total Pages: 148

ISBN-13: 3030012883

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This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

Representation Theory and Algebraic Geometry
Representation Theory and Algebraic Geometry

Author: Vladimir Baranovsky

Publisher: Springer Nature

Published: 2022-06-15

Total Pages: 458

ISBN-13: 3030820076

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The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Perverse Sheaves and Applications to Representation Theory
Perverse Sheaves and Applications to Representation Theory

Author: Pramod N. Achar

Publisher: American Mathematical Soc.

Published: 2021-09-27

Total Pages: 562

ISBN-13: 1470455978

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Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

An Introduction to the Langlands Program
An Introduction to the Langlands Program

Author: Joseph Bernstein

Publisher: Springer Science & Business Media

Published: 2013-12-11

Total Pages: 283

ISBN-13: 0817682260

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This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.

Relative Trace Formulas
Relative Trace Formulas

Author: Werner Müller

Publisher: Springer Nature

Published: 2021-05-18

Total Pages: 438

ISBN-13: 3030685063

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A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.

Geometric Aspects of the Trace Formula
Geometric Aspects of the Trace Formula

Author: Werner Müller

Publisher: Springer

Published: 2018-10-11

Total Pages: 461

ISBN-13: 3319948334

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The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.