Pierre Deligne's Books

L'optique dans les instruments : Applications à la médecine et à la biologie

By: GOURE Jean-Pierre

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L'optique dans les instruments : Applications à la médecine et à la biologie

By: GOURE Jean-Pierre

Les instruments jouent un rôle primordial dans l’avancée scientifique et technologique. Les ouvrages de cette mini-série consacrée à l’optique dans les instruments ont pour but de montrer que l’optique et les composants optiques constituent souvent la partie essentielle autour de laquelle interviennent l’électronique, la mécanique et l’informatique. Le premier tome a décrit les bases nécessaires à la compréhension des phénomènes physiques mis en jeu. Ce second tome a pour but d’illustrer par divers exemples le rôle fondamental de l’optique dans l’instrumentation destinée à la biologie et à la médecine. Sont développés quelques instruments utilisés en routine pour l’analyse et la caractérisation, des instruments de très haute complexité permettant aux chercheurs d’avoir accès à des mesures ultra précises ainsi que des technologies prometteuses actuellement en développement. Enfin ces exemples permettront de voir l’impact des lasers non seulement dans l’instrumentation mais aussi dans les soins médicaux depuis l’ophtalmologie jusqu’à la chirurgie et le traitement de nombreuses maladies.

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274

Publisher

Lavoisier

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ISBN 10

2746295296

ISBN 13

9782746295292

Souvenirs Militaires De La République Et De l’Empire

By: Général Baron Pierre Berthezène

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Souvenirs Militaires De La République Et De l’Empire

By: Général Baron Pierre Berthezène

« Souvenirs militaires de la République et de l’Empire. Paris, Dumaine, 1855, 2 vol. in-8°. Portr. Bon récit de la seconde campagne d’Italie (pp. 85-108) et surtout des opérations en Prusse et de l’occupation du pays : recensement des ressources (donations, problème de la monnaie... (pp. 111-168). Nombreux détails, mais des inexactitudes, sur la campagne d’Autriche (pp. 169-270), l’expédition d’Anvers (pp. 273-283). La guerre en Russie occupe les dernières pages du tome I et le début du tome II. La campagne de 1813 est également racontée de façon détaillée. A peu près rien en revanche sur la campagne de France. Les souvenirs s’achèvent sur les opérations de 1815. C’est par cette partie que Berthezène avait commencé la rédaction de ses mémoires en 1816. Malgré quelques erreurs, il a l’avantage sur d’autres généraux, de s’attacher à décrire les pays occupés ou envahis. » p 16 - Professeur Jean Tulard, Bibliographie Critique Des Mémoires Sur Le Consulat Et L’Empire, Droz, Genève, 1971

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325

Publisher

Pickle Partners Publishing

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ISBN 10

1782891420

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9781782891420

The Navier-Stokes Problem in the 21st Century

By: Pierre Gilles Lemarie-Rieusset

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The Navier-Stokes Problem in the 21st Century

By: Pierre Gilles Lemarie-Rieusset

Praise for the first edition “The author is an outstanding expert in harmonic analysis who has made important contributions. The book contains rigorous proofs of a number of the latest results in the field. I strongly recommend the book to postgraduate students and researchers working on challenging problems of harmonic analysis and mathematical theory of Navier-Stokes equations." —Gregory Seregin, St Hildas College, Oxford University “"This is a great book on the mathematical aspects of the fundamental equations of hydrodynamics, the incompressible Navier-Stokes equations. It covers many important topics and recent results and gives the reader a very good idea about where the theory stands at present.” —Vladimir Sverak, University of Minnesota The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century, Second Edition continues to provide a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.

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778

Publisher

CRC Press

Published Date

ISBN 10

1003807429

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9781003807421

Sheaves on Manifolds

With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel

By: Masaki Kashiwara,Pierre Schapira

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Sheaves on Manifolds

With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel

By: Masaki Kashiwara,Pierre Schapira

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

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522

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Springer Science & Business Media

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ISBN 10

3662026619

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9783662026618

Notes on Crystalline Cohomology. (MN-21)

By: Pierre Berthelot,Arthur Ogus

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Notes on Crystalline Cohomology. (MN-21)

By: Pierre Berthelot,Arthur Ogus

Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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256

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Princeton University Press

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ISBN 10

1400867312

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9781400867318

Topics in Geometric Group Theory

By: Pierre de la Harpe

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Topics in Geometric Group Theory

By: Pierre de la Harpe

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

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320

Publisher

University of Chicago Press

Published Date

ISBN 10

0226317196

ISBN 13

9780226317199

Integrable Systems

Actes Du Colloque International de Luminy

By: Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach

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Integrable Systems

Actes Du Colloque International de Luminy

By: Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach

This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments.

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392

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Springer Science & Business Media

Published Date

ISBN 10

0817636536

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9780817636531

Renormalization and Galois Theories

By: Frédéric Fauvet,Jean-Pierre Ramis

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Renormalization and Galois Theories

By: Frédéric Fauvet,Jean-Pierre Ramis

This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

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284

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190736

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9783037190739

Conformal Groups in Geometry and Spin Structures

By: Pierre Anglès

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Conformal Groups in Geometry and Spin Structures

By: Pierre Anglès

This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.

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307

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Springer Science & Business Media

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ISBN 10

0817635122

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9780817635121

From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

By: Jean-Pierre Marquis

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From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

By: Jean-Pierre Marquis

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

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316

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Springer Science & Business Media

Published Date

ISBN 10

1402093845

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9781402093845

Categories and Sheaves

By: Masaki Kashiwara,Pierre Schapira

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Categories and Sheaves

By: Masaki Kashiwara,Pierre Schapira

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

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496

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Springer Science & Business Media

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ISBN 10

3540279504

ISBN 13

9783540279501

Lectures on N_X(p)

By: Jean-Pierre Serre

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Lectures on N_X(p)

By: Jean-Pierre Serre

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in

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169

Publisher

CRC Press

Published Date

ISBN 10

1466501936

ISBN 13

9781466501935

Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

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Grothendieck-Serre Correspondence

By: Alexandre Grothendieck,Pierre Colmez

The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schernes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.) Also included are a few letters written between 1984 and 1987. The letters are supplemented by J.-P. Serre's notes, which give explanations, corrections, and references further results." "The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created."--BOOK JACKET.

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602

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082183424X

ISBN 13

9780821834244

Abstract" Homomorphisms of Split Kac-Moody Groups"

By: Pierre-Emmanuel Caprace

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Abstract" Homomorphisms of Split Kac-Moody Groups"

By: Pierre-Emmanuel Caprace

This work is devoted to the isomorphism problem for split Kac-Moody groups over arbitrary fields. This problem turns out to be a special case of a more general problem, which consists in determining homomorphisms of isotropic semisimple algebraic groups to Kac-Moody groups, whose image is bounded. Since Kac-Moody groups possess natural actions on twin buildings, and since their bounded subgroups can be characterized by fixed point properties for these actions, the latter is actually a rigidity problem for algebraic group actions on twin buildings. The author establishes some partial rigidity results, which we use to prove an isomorphism theorem for Kac-Moody groups over arbitrary fields of cardinality at least $4$. In particular, he obtains a detailed description of automorphisms of Kac-Moody groups. This provides a complete understanding of the structure of the automorphism group of Kac-Moody groups over ground fields of characteristic $0$. The same arguments allow to treat unitary forms of complex Kac-Moody groups. In particular, the author shows that the Hausdorff topology that these groups carry is an invariant of the abstract group structure. Finally, the author proves the non-existence of cocentral homomorphisms of Kac-Moody groups of indefinite type over infinite fields with finite-dimensional target. This provides a partial solution to the linearity problem for Kac-Moody groups.

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108

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842587

ISBN 13

9780821842584

Galois' Theory Of Algebraic Equations (Second Edition)

By: Jean-pierre Tignol

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Galois' Theory Of Algebraic Equations (Second Edition)

By: Jean-pierre Tignol

The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'group' and 'field'. A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.

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325

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9814704717

ISBN 13

9789814704717

Atlantida

(Annotated)

By: Pierre Benoit

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Atlantida

(Annotated)

By: Pierre Benoit

Now with an Historical Afterword by Ron Miller Featured in Ron Miller's The Conquest of Space Book Series. In this classic Atlantean novel by Pierre Benoit, two adventurous soldiers discover the remnants of Atlantis deep in the Sahara Desert...as well as the chilling secret of its deadly, immortal queen, Antinea. Originally published in 1920. At the publisher's request, this title is sold without DRM (Digital Rights Management).

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222

Publisher

Baen Publishing Enterprises

Published Date

ISBN 10

162579049X

ISBN 13

9781625790491

Cohomological Invariants in Galois Cohomology

By: Skip Garibaldi,Alexander Merkurjev,Jean-Pierre Serre

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Cohomological Invariants in Galois Cohomology

By: Skip Garibaldi,Alexander Merkurjev,Jean-Pierre Serre

This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here. The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number th

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178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832875

ISBN 13

9780821832875

Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps

By: Pierre Albin,Frédéric Rochon,David Sher

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Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps

By: Pierre Albin,Frédéric Rochon,David Sher

Manifolds with ﬁbered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coeﬃcients in a ﬂat bundle on a closed manifold undergoing degeneration to a manifold with ﬁbered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with ﬁbered cusps in terms of the R-torsion of the underlying manifold with boundary.

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126

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470444224

ISBN 13

9781470444228

Linear Representations of Finite Groups

By: Jean-Pierre Serre

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Linear Representations of Finite Groups

By: Jean-Pierre Serre

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

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178

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Springer Science & Business Media

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ISBN 10

1468494589

ISBN 13

9781468494587

Topics in Galois Theory

By: Jean-Pierre Serre

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Topics in Galois Theory

By: Jean-Pierre Serre

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi

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120

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CRC Press

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ISBN 10

1439865256

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9781439865255

Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

By: Pierre Magal,Shigui Ruan

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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

By: Pierre Magal,Shigui Ruan

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.

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American Mathematical Soc.

Published Date

ISBN 10

0821846531

ISBN 13

9780821846537

Abelian l-Adic Representations and Elliptic Curves

By: Jean-Pierre Serre

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Abelian l-Adic Representations and Elliptic Curves

By: Jean-Pierre Serre

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one

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203

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CRC Press

Published Date

ISBN 10

1439863865

ISBN 13

9781439863862

Geometric Topology: Recent Developments

Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- tini Terme, Italy, June 4-12, 1990

By: Jeff Cheeger,Mikhail Gromov,Christian Okonek,Pierre Pansu

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Geometric Topology: Recent Developments

Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- tini Terme, Italy, June 4-12, 1990

By: Jeff Cheeger,Mikhail Gromov,Christian Okonek,Pierre Pansu

Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex,algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semi-simple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of low-dimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry.- M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction.- Chr. Okonek: Instanton Invariants and Algebraic Surfaces.

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204

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Springer

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ISBN 10

3540466517

ISBN 13

9783540466512

Freedom in Mathematics

By: Pierre Cartier,Jean Dhombres,Gerhard Heinzmann,Cédric Villani

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Freedom in Mathematics

By: Pierre Cartier,Jean Dhombres,Gerhard Heinzmann,Cédric Villani

This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.

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128

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Springer

Published Date

ISBN 10

8132227883

ISBN 13

9788132227885

Queen of Atlantis

By: Pierre Beno‘t

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Queen of Atlantis

By: Pierre Beno‘t

In 1903 Lieutenant Olivier Ferri_res of the French army welcomes Captain de Saint-Avit as the new commandant of his post in Algeria. Shunned by his fellow officers, the captain has been accused of the brutal murder of his friend Lieutenant Morhange, when the two were lost alone in the desert. To Ferri_res?s horror, Saint-Avit soon confesses to the crime, unveiling a shocking tale of lost worlds, lust, murder, and the enslavement of desire in a forgotten desert kingdom?Atlantis! Antinea, the queen of Atlantis, seeks to destroy and imprison the men in her net through her beauty and cruelty, enshrining their electroplated bodies in a fantastic hall, assigning each doomed lover a number and a plaque in his memory. Caught in this web, Saint-Avit and Morhange attempt to escape until love, passion, and jealousy threaten their friendship and their very lives. For only one man has ever captured the heart of Antinea, and no one escapes the queen of Atlantis.

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316

Publisher

U of Nebraska Press

Published Date

ISBN 10

0803269161

ISBN 13

9780803269163

Regular and Irregular Holonomic D-Modules

By: Masaki Kashiwara,Pierre Schapira

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Regular and Irregular Holonomic D-Modules

By: Masaki Kashiwara,Pierre Schapira

A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.

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119

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Cambridge University Press

Published Date

ISBN 10

1316613453

ISBN 13

9781316613450

Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

By: Nicolas Bergeron,Pierre Charollois,Luis E. Garc¡a

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Cocycles de groupe pour $mathrm {GL}_n$ et arrangements d?hyperplans

By: Nicolas Bergeron,Pierre Charollois,Luis E. Garc¡a

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

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146

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American Mathematical Society, Centre de Recherches Math‚matiques

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ISBN 10

1470474115

ISBN 13

9781470474119

Oeuvres - Collected Papers

Volume 3: 1972 - 1984

By: Jean-Pierre Serre

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Oeuvres - Collected Papers

Volume 3: 1972 - 1984

By: Jean-Pierre Serre

From the reviews of Vols. I-III: "Since their publication in 1986 J-P. Serre's Collected Papers have already become one of the classical references in mathematical research. This is on the one hand due to the completeness of the collection (132 items) and on the other, of course, due to the beautiful and clear expositions of Serre's papers and their influence on mathematics. As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published. [...] The author's notes at the end of each volume giving corrections and important recent progress as well as improvements of the main results represent a highlight of this collection. The mathematical community definitely looks forward to further volume(s) of Serre's outstanding work." Zentralblatt MATH

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750

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Springer Science & Business Media

Published Date

ISBN 10

3540435646

ISBN 13

9783540435648

Book's by Pierre Deligne

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