ISBN: 978-2-85629-263-1
Series: Asterisque, Number 323
Published: 15 April 2010; Copyright Year: 2009; Pages: 487; Softcover
Graduate students and research mathematicians interested in differential equations and singularities.
This volume contains 23 papers about “Differential Equations and Singularities” written on the occasion of the congress in honour of J.M. Aroca, which took place at the University of Valladolid on September 4-8, 2006.
F. A. Cuesta, A. L. Rojo, and M. M. Stadler -- Dynamique transverse de la lamination de Ghys-Kenyon
C. Beddani -- Comparaison des valuations divisorielles
F. E. Brochero Martinez and L. Lopez-Hernanz -- Gevrey class of the infinitesimal generator of a diffeomorphism
C. Camacho and L. H. de Figueiredo -- On the limit of families of algebraic subvarieties with unbounded volume
J. Cano and P. F. Ayuso -- The space of generalized formal power series solution of an ordinary differential equation
G. Casale -- Une preuve galoisienne de l'irredictibilite au sens de Nishioka-Umemura de la premiere equation de Painleve
D. Cerveau -- Feuilletages en droites, equations des eikonales et autres equations differentielles
M. Chaperon and S. L. de Medrano -- Some regularities and singularities appearing in the study of polynomials and operators
N. Corral -- Polar pencil of curves and foliations
A. L. Neto -- Homogeneous commuting vector fields on mathbb{C}^2
J.-M. Lion and P. Speissegger -- Un theoreme de type Haefliger definissable
F. Loray and D. M. Perez -- Projective structures and projective bundles over compact Riemann surfaces
R. Moussu and J.-P. Rolin -- Une preuve combinatoire du theoreme de Frobenius
P. Fernandez-Sanchez and J. Mozo-Fernandez -- On generalized surfaces in (mathbb{C}^3,0)
E. Paul -- The Galoisian envelope of a germ of foliation: the quasi-homogeneous case
J. V. Pereira and P. Sad -- Rigidity of fibrations
J.-P. Ramis and J. Sauloy -- The q-analogue of the wild fundamental group (II)
J. Ribon -- Unfoldings of tangent to the identity diffeomorphisms
G. Rond -- Series de Poincare motiviques d'un germe d'hypersurface irreductible quasi-ordinaire
J. Sauloy -- Equations aux q-differences et fibres vectoriels holomorphes sur la courbe elliptique mathbb{C}^ast/q^{mathbb{Z}}
M. G. Soares -- Singularities of logarithmic foliations and connectedness of the union of logarithmic components
H. Umemura -- On the definition of the Galois groupoid
J. van der Hoeven -- Transserial Hardy fields
ISBN: 978-2-85629-264-8
Asterisque, Number 324
Published: 15 April 2010; Copyright Year: 2009; Pages: 314; Softcover
Graduate students and research mathematicians interested in number theory.
This book presents an in-depth study of the families of Galois representations
carried by the p -adic eigenvarieties attached to unitary groups. The study
encompasses some general algebraic aspects (properties of the space of
representations of a group in the neighborhood of a point, reducibility
loci, pseudocharacters), and other aspects more specific to Galois groups
of local or number fields. In particular, the authors define and study
certain deformation functors of crystalline representations of the absolute
Galois group of Q p , namely trianguline deformations, which are naturally
associated to the families above.
As an application, the authors show how the geometry of these eigenvarieties at “classical” points is related to the dimension of certain Selmer groups.
This, combined with conjectures of Langlands and Arthur on the discrete
automorphic spectrum of unitary groups, allows the authors to prove, among
other things, new cases of the Bloch-Kato conjectures (in any dimension).
Introduction
Pseudocharacters, representations and extensions
Trianguline deformations of refined crystalline representations
Generalization of a result of Kisin on crystalline periods
Rigid analytic families of refined p-adic representations
Selmer groups and a conjecture of Bloch-Kato
Automorphic forms on definite unitary groups: results and conjectures
Eigenvarieties of definite unitary groups
The sign conjecture
The geometry of the eigenvariety at some Arthur points and higher rank Selmer groups
Appendix: Arthur's conjectures
Bibliography
Index of notations
ISBN: 978-2-85629-266-2
Series: Asterisque, Number 325
Published: 15 April 2010; Copyright Year: 2009; Pages: 139; Softcover
Graduate students and research mathematicians interested in geometry and topology.
Motivated by the dynamics of rational maps, the authors introduce a class
of topological dynamical systems satisfying certain topological regularity,
expansion, irreducibility, and finiteness conditions. The authors call
such maps “topologically coarse expanding conformal” (top. CXC) dynamical
systems.
Given such a system f : X → X and a finite cover of X by connected open
sets, the authors construct a negatively curved infinite graph on which
f acts naturally by local isometries.
The induced topological dynamical system on the boundary at infinity is
naturally conjugate to the dynamics of f . This implies that X inherits
metrics in which the dynamics of f satisfies the Principle of the Conformal
Elevator: arbitrarily small balls may be blown up with bounded distortion
to nearly round sets of definite size. This property is preserved under
conjugation by a quasisymmetric map, and (top. CXC) dynamical systems on
a metric space satisfying this
property the authors call “metrically CXC”. The ensuing results deepen
the analogy between rational maps and Kleinian groups by extending it to
analogies between metric CXC systems and hyperbolic groups.
The authors give many examples and several applications. In particular,
they provide a new interpretation of the characterization of rational functions
among topological maps and of generalized Lattes examples among uniformly
quasiregular maps. Via techniques in the spirit of those used to construct
quasiconformal measures for hyperbolic groups, the authors also establish
existence, uniqueness, naturality, and metric regularity properties for
the measure
of maximal entropy of such systems.
Introduction
Coarse expanding conformal dynamics
Geometrization
Expanding non-invertible dynamics
A. Quasiconformal analysis
B. Hyperbolic groups in a nutshell
Bibliography
Index
Table of symbols
ISBN: 978-2-85629-269-3
Series: Asterisque, Number 326
Published: 15 April 2010; Copyright Year: 2009; Pages: 409; Softcover
Graduate students and research mathematicians interested in many different areas of mathematics.
As in the preceding volumes of this seminar, one finds here fifteen survey lectures on topics of current interest: four lectures on algebraic geometry, one on number theory, one on probability theory, four on differential geometry, three about groups or Lie algebras, one concerning dynamical systems, and one about mathematical physics.
Novembre 2007
S. Druel -- Existence de modeles minimaux pour les varietes de type general
P. Gille -- Le probleme de Kneser-Tits
B. Remy -- Covolume des groupes S-arithmetiques et faux plans projectifs
A. J. Wilkie -- o-minimal structures
D. Zagier -- Ramanujan's mock theta functions and their applications
Mars 2008
P. Cartier -- Groupoides de Lie et leurs algebroides
L. H. Eliasson -- Resultats non-perturbatifs pour l'equation de Schrodinger et d'autres cocycles quasi-periodiques
C. Gasbarri -- The strong abc conjecture over function fields
M. Ledoux -- Geometrie des espaces metriques mesures: les travaux de Lott, Villani, Sturm
M. Pun -- Courants d'Ahlfors et localisation des courbes entieres
Juin 2008
V. Beffara -- Grands graphes planaires aleatoires et carte brownienne
P. Haissinsky -- Geometrie quasiconforme, analyse au bord des espaces metriques hyperboliques et rigidites
C. Pauly -- La dualite etrange
B. Poizat -- Amalgames de Hrushovski
J.-C. Yoccoz -- Echanges d'intervalles et surfaces de translation
ISBN: 978-2-85629-283-9
Series: Asterisque, Number 329
Published: 15 May 2010; Copyright Year: 2010; Pages: 172; Softcover
Graduate students and research mathematicians interested in probability.
This text defines and studies a class of stochastic processes indexed by
curves drawn on a compact surface and taking their values in a compact
Lie group. The author calls these processes two-dimensional Markovian holonomy
fields. The prototype of these processes, and the only one to have been
constructed before the present work, is the canonical process under the
Yang-Mills measure, first defined by Ambar Sengupta and later by the author.
The Yang-Mills measure sits in the class of Markovian holonomy fields very
much like the Brownian motion in the class of Levy processes.
The author proves that every regular Markovian holonomy field determines
a Levy process of a certain class on the Lie group in which it takes its
values, and he constructs, for each Levy process in this class, a Markovian
holonomy field to which it is associated. When the Lie group is in fact
a finite group, the author gives an alternative construction of this Markovian
holonomy field as the monodromy of a random ramified principal bundle.
Heuristically, this agrees with the physical origin of the Yang-Mills measure
as the holonomy of a random connection on a principal bundle.
Introduction
Surfaces and graphs
Multiplicative processes indexed by paths
Markovian holonomy fields
Levy processes and Markovian holonomy fields
Random ramified coverings
Index
Bibliography
ISBN: 978-2-85629-281-5
Series: Asterisque, Number 330
Published: 15 May 2010; Copyright Year: 2010; Pages: 554; Softcover
Graduate students and research mathematicians interested in number theory.
This second volume is devoted to applications of Fontaine’s theory of (? , Γ )-modules to that of p -adic unitary representations of GL2 (Qp ), whose aim is to construct a (p -adic local Langlands) correspondence between these representations and 2-dimensional p -adic representations of the absolute Galois group of Qp . In this volume the reader will find an overview of classical p -adic functional analysis, diverse features of the unitary principal series of GL2 (Qp ), and the construction of functors building bridges between the world of Galois representations and that of representations of GL2 (Qp ) and its mirabolic subgroup.
M.-F. Vigneras -- Banach ell-adic representations of p-adic groups
P. Colmez -- Fonctions d'une variable p-adique
P. Colmez -- (varphi, Gamma)-modules et representations du mirabolique de mathbf{GL}_2(mathbf{Q}_p)
L. Berger and C. Breuil -- Sur quelques representations potentiellement cristallines de mathrm{GL}_2(mathbf{Q}_p)
P. Colmez -- La serie principale unitaire de mathbf{GL}_2(mathbf{Q}_p)
L. Berger -- Representations modulaires de mathrm{GL}_2(mathbf{Q}_p) et representations galoisiennes de dimension 2
P. Colmez -- Representations de mathbf{GL}_2(mathbf{Q}_p) et (varphi, Gamma)-modules
M. Kisin -- Deformations of G_{mathbb{Q}_p} and mathrm{GL}_2(mathbb{Q}_p) representations
G. Bockle -- Deformation rings for some mod 3 Galois representations of the absolute Galois group of mathbf{Q}_3
F. Andreatta and A. Iovita -- Erratum to the article: Global applications to relative (varphi,Gamma)-modules, I