ISBN: 978-3-03719-186-6
Series, Volume: EMS Series of Congress Reports, Volume 14
Bibliographic Information: Published: 30 June 2018; Copyright Year: 2018; Pages: 436;
Hardcover;
Subject Classification
Algebra and Algebraic Geometry
Differential Equations
Scientists active in the covered fields.
This volume is dedicated to Helge Holden on the occasion of his 60th anniversary.
It collects contributions by numerous scientists with expertise in non-linear partial differential
equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree
Helge Holdenfs longstanding research interests.
Accordingly, the problems addressed in the contributions deal with a large range of topics,
including, in particular, infinite-dimensional analysis, linear and nonlinear PDEs, stochastic
analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic
dynamics and sestina poetry. They represent to some extent the lectures presented at the conference
Non-linear PDEs, Mathematical Physics and Stochastic Analysis, held at the Norwegian
University of Science and Technology, Trondheim, July 4?7, 2016.
The mathematical tools involved draw from a wide variety of techniques in functional analysis,
operator theory, and probability theory. This collection of research papers will be of interest to
any active scientist working in one of the above-mentioned areas.
ISBN: 978-3-03719-188-0
Series, Volume: EMS Textbooks in Mathematics, Volume 21
Bibliographic Information: Published: 30 June 2018; Copyright
Year: 2018; Pages: 168; Hardcover;
Subject Classification
Discrete Mathematics and Combinatorics Number Theory
Undergraduate and graduate students and researchers interested in linear algebra
and group theory.
Spectral graph theory starts by associating matrices to graphs?notably, the adjacency
matrix and the Laplacian matrix. The general theme is then, first, to compute or estimate
the eigenvalues of such matrices, and, second, to relate the eigenvalues to structural properties
of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications
concern facts that are, in principle, purely graph theoretic or combinatorial.
This text is an introduction to spectral graph theory, but it could also be seen as an invitation
to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come
together. This part provides an appealing motivation and context for the second spectral half.
The text is enriched by many exercises and their solutions.
The target audience is students at the upper undergraduate level and above. The book only
assumes a familiarity with linear algebra and basic group theory. Graph theory, finite fields,
and character theory for abelian groups receive a concise overview and render the text essentially
self-contained.
ISBN: 978-3-03719-189-7
Series, Volume: Zurich Lectures in Advanced Mathematics, Volume 24
Bibliographic Information: Published: 30 June 2018; Copyright Year:
2018; Pages: 160; Softcover
Algebra and Algebraic Geometry
Readership: Graduate students and researchers in geometric group
theory, algebra, and combinatorics.
Coxeter groups are groups generated by reflections. They appear throughout mathematics.
Tits developed the general theory of Coxeter groups in order to develop the theory of
buildings. Buildings have interrelated algebraic, combinatorial and geometric structures and are
powerful tools for understanding the groups which act on them.
These notes focus on the geometry and topology of Coxeter groups and buildings, especially
nonspherical cases. The emphasis is on geometric intuition, and there are many examples and
illustrations. Part I describes Coxeter groups and their geometric realizations, particularly the
Davis complex, and Part II gives a concise introduction to buildings.
This book will be suitable for graduate students and researchers in geometric group theory, as
well as algebra and combinatorics. The assumed background is basic group theory, including
group actions, and basic algebraic topology, together with some knowledge of Riemannian
geometry.
ISBN: 978-2-85629-880-0
Series, Volume: Asterisque, Number 397
Bibliographic Information: Published: 1 May 2018; Copyright Year:
2018; Pages: 184; Softcover;
Algebra and Algebraic Geometry
Graduate students and research mathematicians.
In this book, the authors propose a new approach to tilting modules for reductive
algebraic groups in positive characteristic. They conjecture that translation functors give an
action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block.
Their conjecture implies character formulas for the simple and tilting modules in terms of
the p -canonical basis, as well as a description of the principal block as the antispherical quotient
of the Hecke category. The authors prove their conjecture for GLn (k) using the theory of
2-Kac-Moody actions.
Finally, the authors prove that the diagrammatic Hecke category of a general crystallographic
Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding
Kac-Moody group.
Memoires de la SMF 154 (2017), 138 pages
Crochets dans les algebres de Pontryagin des varietes
Un objet geometrique fondamental qu'on associe a tout espace topologique M avec un point marque est son espace de lacets bases en . L'algebre de Pontryagin A de (M,) est l'homologie singuliere de cet espace de lacets, avec sa structure d'algebre graduee induite par la multiplication usuelle des lacets. Lorsque M est une variete orientee lisse a bord et est choisi sur M, nous definissons une operation ``d'intersection'' AA AA. Nous prouvons que cette operation est un crochet double au sens de Michel Van den Bergh satisfaisant une variante de l'identite de Jacobi. Nous montrons que ce crochet double induit des crochets de Grstenhaber sur les algebres de representations de A. Ceci etend notre precedent travail sur les surfaces, ou A est l'algebre de groupe du groupe fondamental d'une surface et les crochets de Gerstenhaber en question sont les crochets de Poisson habituels sur les espaces de modules de representations d'un tel groupe. Le present travail est inspire des resultats de William Goldman sur les surfaces, et des idees de la topologie des cordes due a Moira Chas et Dennis Sullivan.
Mots-clefs : Smooth manifold, intersection pairing, string topology, loop space, Pontryagin algebra, Poisson bracket, Gerstenhaber bracket, noncommutative Poisson structure, double bracket
A fundamental geometric object derived from an arbitrary topological space
M with a marked point is the space of loops in M based at . The Pontryagin
algebra A of (M,) is the singular homology of this loop space with the
graded algebra structure induced by the standard multiplication of loops.
When M is a smooth oriented manifold with boundary and is chosen on M,
we define an ``intersection'' operation AA AA. We prove that this operation
is a double bracket in the sense of Michel Van den Bergh satisfying a version
of the Jacobi identity. We show that our double bracket induces Gerstenhaber
brackets in the representation algebras of A. These results extend our
previous work on surfaces, where A is the group algebra of the fundamental
group of a surface and the Gerstenhaber brackets in question are the usual
Poisson brackets on the moduli spaces of representations of such a group.
The present work is inspired by the results of William Goldman on surfaces
and by the ideas of string topology due to Moira Chas and Dennis Sullivan.
Keywords: Smooth manifold, intersection pairing, string topology, loop space, Pontryagin algebra, Poisson bracket, Gerstenhaber bracket, noncommutative Poisson structure, double bracket
Class. math. : 17B63, 55N33, 55P50, 57R19
ISBN : 978-2-85629-876-3
DOI : 10.24033/msmf.462
Publie avec le concours de : Centre National de la Recherche Scientifique
Memoires de la SMF 155 (2017), viii+245 pages
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On etudie les formes modulaires p-adiques sur les courbes de Shimura unitaires et montre l'existence des formes compagnons surconvergentes en utilisant les theoremes de comparaison p-adique. Ceci, combine avec des resultats sur les representations localement analytiques de GL_2(L), nous permet d'obtenir des resultats de compatibilite local-global sur le socle localement analytique dans le H^1-complete des courbes de Shimura unitaires. En outre, en utilisant une loi d'adjonction en famille du foncteur de Jacquet-Emerton et la theorie de triangulation globale, on montre egalement des resultats de compatibilite local-global sur des representations localement analytiques non semi-simples.
Mots-clefs : Cohomologie completee, compatibilite local-global, courbe de Shimura unitaire, forme modulaire p-adique, programme de Langlands p-adique, representation localement analytique, variete de Hecke
p-adic modular forms over unitary Shimura curves and local-global compatibility
We study p-adic modular forms over unitary Shimura curves and prove the existence of overconvergent companions forms over unitary Shimura curves using p-adic comparison theorems. From which, together with some locally analytic representation theory of GL_2(L), we deduce some local-global compatibility results on the socle for the completed H^1 of unitary Shimura curves. In addition, using an adjunction formula for Jacquet-Emerton functor in family and global triangulation theory, we also prove some local-global compatibility results for non semi-simple locally analytic representations.
Keywords: p-adic Langlands programme, local-global compatibility, GL_2(L), crystalline representation, unitary Shimura curve, locally analytic representation, eigenvariety, p-adic family of Galois representations, p-adic modular form, overconvergent companion form.
Class. math. : 14F41, 11F85, 22E50
ISBN : 978-2-85629-877-0
ISSN : 0249-633X (print) 2275-3230 (electronic)
DOI : 10.24033/msmf.463
Publie avec le concours de : Centre National de la Recherche Scientifique
Jean-Christophe Yoccoz aurait eu 60 ans le 29 mai 2017. Nous avions prevu dforganiser un colloque a cette occasion, mais rattrape par la maladie il nous a quittes en septembre 2016. Nous avons decide de maintenir cette conference a sa memoire : elle sfest tenue au College de France a la fin du mois de mai 2017 et a rassemble plus de 250 personnes. Apres trois jours dfexposes sur les themes de recherche qui lui etaient chers, ce colloque sfest cloture sur une journee au cours de laquelle des collegues, eleves, amis... se sont succede pour parler de lfhomme et du mathematicien. Ce numero special de la Gazette prolonge cette journee dfhommage.
Preface
Dynamique de populations de petits mammiferes, saisonnalite et attracteur de Henon ? S. Arlot et al.
De Michel a Jean-Christophe ? M.-C. Arnaud
Une breve histoire de Jean-Christophe ? P. Arnoux et al.
The early bird ? A. Avila
Un eleve a lfecole dfun maitre ? P. Berger
La connexite locale de lfensemble de Mandelbrot ? X. Buff
Linearisation des polynomes quadratiques selon Jean-Christophe Yoccoz ? A. Cheritat
Un probleme pour le XXI(I)e siecle ? S. Crovisier et S. Senti
Le volcan maitrise ? R. Douady
J.-C. Yoccoz and the theory of circle diffeomorphisms ? H. Eliasson, B. Fayad et R. Krikorian
Un souvenir ? M. Flexor
Deux souvenirs du jeune Jean-Christophe ? E. Ghys
Jean-Christophe Yoccoz et la diffusion des mathematiques ? J.-P. Kahane
Jean-Christophe, neveu dans la famille mathematicienne ? F. Laudenbach
Jean-Christophe : du lycee au College ? P.-L. Lions
Fonctions de Brjuno, echanges dfintervalles, origamis et autres objets insolites ? S. Marmi, C. Matheus et P. Moussa
Homoclinic bifurcations : our collaboration with Jean-Christophe Yoccoz ? C. G. Moreira et J. Palis
Chers souvenirs de Jean-Christophe ? R. Perez-Marco
Memories of Jean-Christophe Yoccoz ? J. Rivera
Les autres Jean-Christophe ? M. Schoenauer
Un hommage a Jean-Christophe, directeur de these ? S. Senti
My dynamics courses at Orsay and Jean-Christophe ? M. Shub
A mathematician, normal and wonderful ? D. Sullivan
ISBN : 978-2-85629-879-4
Prix public : 25 euro
Prix membre SMF : 18 euro
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