Relative Aspects In Representation Theory Langlands Functoriality And Automorphic Forms

Author : Volker Heiermann,Dipendra Prasad
Publisher : Springer
Page : 364 pages
File Size : 47,6 Mb
Release : 2018-10-01
Category : Mathematics
ISBN : 9783319952314

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Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms by Volker Heiermann,Dipendra Prasad Pdf

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.

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Birkhäuser
Page : 214 pages
File Size : 48,5 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0817671293

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

Author : Helge Holden,Ragni Piene
Publisher : Springer Nature
Page : 876 pages
File Size : 47,8 Mb
Release : 2024
Category : Computer science
ISBN : 9783031339738

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The Abel Prize 2018-2022 by Helge Holden,Ragni Piene Pdf

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.

Author : Wen-Wei Li
Publisher : Springer
Page : 148 pages
File Size : 47,7 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783030012885

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Zeta Integrals, Schwartz Spaces and Local Functional Equations by Wen-Wei Li Pdf

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.

Author : Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Publisher : Springer Nature
Page : 458 pages
File Size : 42,6 Mb
Release : 2022-06-15
Category : Mathematics
ISBN : 9783030820077

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Representation Theory and Algebraic Geometry by Vladimir Baranovsky,Nicolas Guay,Travis Schedler Pdf

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.

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 41,9 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

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.

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Birkhäuser
Page : 214 pages
File Size : 47,6 Mb
Release : 2007-10-31
Category : Mathematics
ISBN : 0817645055

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

Author : Jayce R. Getz
Publisher : Springer Nature
Page : 611 pages
File Size : 51,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783031411533

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An Introduction to Automorphic Representations by Jayce R. Getz Pdf

Author : Werner Müller,Sug Woo Shin,Nicolas Templier
Publisher : Springer Nature
Page : 438 pages
File Size : 54,6 Mb
Release : 2021-05-18
Category : Mathematics
ISBN : 9783030685065

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Relative Trace Formulas by Werner Müller,Sug Woo Shin,Nicolas Templier Pdf

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.

Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 46,6 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540390558

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Automorphic Forms on GL (3,TR) by D. Bump Pdf

Author : Werner Müller,Sug Woo Shin,Nicolas Templier
Publisher : Springer
Page : 453 pages
File Size : 45,6 Mb
Release : 2018-10-11
Category : Mathematics
ISBN : 9783319948331

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Geometric Aspects of the Trace Formula by Werner Müller,Sug Woo Shin,Nicolas Templier Pdf

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.

Author : T. N. Bailey,Anthony W. Knapp
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 54,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806098

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Representation Theory and Automorphic Forms by T. N. Bailey,Anthony W. Knapp Pdf

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 279 pages
File Size : 51,8 Mb
Release : 1975-03-21
Category : Mathematics
ISBN : 9780691081564

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Automorphic Forms on Adele Groups by Stephen S. Gelbart Pdf

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Author : T. N. Bailey,Anthony W. Knapp
Publisher : American Mathematical Soc.
Page : 496 pages
File Size : 43,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821868349

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Representation Theory and Automorphic Forms by T. N. Bailey,Anthony W. Knapp Pdf

This book is a course in representation theory of semisimple groups, automorphic forms, and the relations between these two subjects, written by some of the world's leading experts in these fields. It is based on the 1996 instructional conference of the International Centre for Mathematical Sciences in Edinburgh. The book begins with an introductory treatment of structure theory and ends with an essay be Robert Langlands on the current status of functoriality. All papers areintended to provide overviews of the topics they address, and the authors have supplied extensive bibliographies to guide the reader who wants more detail.The aim of the articles is to treat representation theory with two goals in mind: i) to help analysts make systematics use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics, and ii) to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem.

Author : Joseph Bernstein,Stephen Gelbart
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 40,8 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780817682262

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An Introduction to the Langlands Program by Joseph Bernstein,Stephen Gelbart Pdf

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.