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Author: Jean-Pierre Labesse
Publisher: American Mathematical Soc.
ISBN: 0821894412
Category : Mathematics
Languages : en
Pages : 264
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Book Description
La formule des traces pour un groupe reductif connexe arbitraire est due a James Arthur. Le cas tordu a fait l'objet du Friday Morning Seminar a l'Institute for Advanced Study de Princeton pendant l'annee academique 1983-1984. Lors de ce seminaire, des ex
Author: Jean-Pierre Labesse
Publisher: American Mathematical Soc.
ISBN: 0821894412
Category : Mathematics
Languages : en
Pages : 264
Get Book Here
Book Description
La formule des traces pour un groupe reductif connexe arbitraire est due a James Arthur. Le cas tordu a fait l'objet du Friday Morning Seminar a l'Institute for Advanced Study de Princeton pendant l'annee academique 1983-1984. Lors de ce seminaire, des ex
Author: Werner Müller
Publisher: Springer
ISBN: 3319948334
Category : Mathematics
Languages : en
Pages : 461
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Book Description
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: Chung Pang Mok
Publisher: American Mathematical Soc.
ISBN: 1470410419
Category : Mathematics
Languages : en
Pages : 260
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Book Description
In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
Author: Helge Holden
Publisher: Springer Nature
ISBN: 3031339738
Category : Computer science
Languages : en
Pages : 876
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Book Description
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: Nicolas Bergeron
Publisher: American Mathematical Society, Centre de Recherches Math‚matiques
ISBN: 1470474115
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Ce livre constitue un expos‚ d‚taill‚ de la s‚rie de cours donn‚s en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montr‚al. L'objet de ce texte est une ample g‚n‚ralisation d'une famille d'identit‚s classiques, notamment la formule d'addition de la fonction cotangente ou celle des s‚ries d'Eisenstein. Le livre relie ces identit‚s … la cohomologie de certains sous-groupes arithm‚tiques du groupe lin‚aire g‚n‚ral. Il rend explicite ces relations au moyen de la th‚orie des symboles modulaires de rang sup‚rieur, d‚voilant finalement un lien concret entre des objets de nature topologique et alg‚brique. This book provides a detailed exposition of the material presented in a series of lectures given in 2020 by Prof. Nicolas Bergeron while he held the Aisenstadt Chair at the CRM in Montr‚al. The topic is a broad generalization of certain classical identities such as the addition formulas for the cotangent function and for Eisenstein series. The book relates these identities to the cohomology of arithmetic subgroups of the general linear group. It shows that the relations can be made explicit using the theory of higher rank modular symbols, ultimately unveiling a concrete link between topological and algebraic objects. I think that the text ?Cocycles de groupe pour $mathrm{GL}_n$ et arrangements d'hyperplans? is terrific. I like how it begins in a leisurely, enticing way with an elementary example that neatly gets to the topic. The construction of these ?meromorphic function?-valued modular symbols are fundamental objects, and play (and will continue to play) an important role. ?Barry Mazur, Harvard University
Author: Yuval Z. Flicker
Publisher: Birkhäuser
ISBN: 3319315935
Category : Mathematics
Languages : en
Pages : 573
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Book Description
This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals.bribr/i/idiviiArthur’s Invariant Trace Formula and Comparison of Inner Forms/div
Author: Gaëtan Chenevier
Publisher: Springer
ISBN: 3319958917
Category : Mathematics
Languages : en
Pages : 428
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Book Description
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Author: Libor Šnob
Publisher: American Mathematical Soc.
ISBN: 147043654X
Category : Mathematics
Languages : en
Pages : 321
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Book Description
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.
Author: Pierre Jacob
Publisher: Oxford University Press, USA
ISBN: 9780198509202
Category : Psychology
Languages : en
Pages : 287
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Book Description
Cognitive neuroscience is a young field that has been incredibly successful in furthering our understanding of the human brain. Long before the emergence of this field, many of the same questions being posed within this field were asked by philosophers. So how much of this earlier work informs current theories of cognition? In many cases--too little. Yet how can we ignore thousands of years of philosophical thinking on the human mind? There are some questions about the human brain that are surely impossible to answer without considering what it "feels" like to see, what it "feels" like to think. Ways of Seeing is a unique collaboration between an eminent philosopher and a world famous neuroscientist. It focuses on one of the most basic human functions--vision. What does it mean to 'see'? It brings together electrophysiological studies, neuropsychology, psychophysics, cognitive psychology, and philosophy of mind. The first truly interdisciplinary book devoted to the topic of vision, this is a book will make a valuable contribution to the field of cognitive science.
Author: Panagiotis Sotiris
Publisher: BRILL
ISBN: 9004291369
Category : Political Science
Languages : en
Pages : 566
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Book Description
In A Philosophy for Communism: Rethinking Althusser Panagiotis Sotiris attempts a reading of the work of the French philosopher centered upon his deeply political conception of philosophy. Althusser’s endeavour is presented as a quest for a new practice of philosophy that would enable a new practice of politics for communism, in opposition to idealism and teleology. The central point is that in his trajectory from the crucial interventions of the 1960s to the texts on aleatory materialism, Althusser remained a communist in philosophy. This is based upon a reading of the tensions and dynamics running through Althusser’s work and his dialogue with other thinkers. Particular attention is paid to crucial texts by Althusser that remained unpublished until relatively recently. Shortlisted for the Deutscher Memorial Prize 2021.
