Series: Universitext
2007, XVIII, 382 p., 12 illus., Softcover
ISBN: 978-0-387-34171-2
About this textbook
This book uses a distinctly applied framework to present the most
important topics in stochastic processes, including Gaussian and
Markovian processes, Markov Chains, Weiner and Poisson processes,
Brownian motion and queueing theory. The book also examines in
detail special diffusion processes, with implications for
finance, doubly stochastic processes, and renewal processes. It
contains numerous examples and approximately 350 advanced
problems that reinforce both concepts and applications. The book
includes statistical tables and solutions to all the even-numbered
problems.
Table of contents
Preface.- Review of probability theory.- Stochastic processes.-
Markov chains.- Diffusion processes.- Poisson processes.-
Queueing theory.- Appendix A. Statistical tables.- Appendix B.
Answers to even-numbered exercises.- References.- Index
Series: Modern Birkhauser Classics
Originally published as volume 152 in the series: Progress in
Mathematics Original French edition published with the title:
Structures Metriques des Varietes Riemanniennes
1st ed. 1999. Corr. 2nd printing 2001. 3rd printing, 2007, XX,
586 p., 100 illus., Softcover
ISBN: 978-0-8176-4582-3
About this book
Metric theory has undergone a dramatic phase transition in the
last decades when its focus moved from the foundations of real
analysis to Riemannian geometry and algebraic topology, to the
theory of infinite groups and probability theory.
The new wave began with seminal papers by Svarc and Milnor on the
growth of groups and the spectacular proof of the rigidity of
lattices by Mostow. This progress was followed by the creation of
the asymptotic metric theory of infinite groups by Gromov.
The structural metric approach to the Riemannian category,
tracing back to Cheeger's thesis, pivots around the notion of the
Gromov?Hausdorff distance between Riemannian manifolds. This
distance organizes Riemannian manifolds of all possible
topological types into a single connected moduli space, where
convergence allows the collapse of dimension with unexpectedly
rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov
and Perelman. Also, Gromov found metric structure within homotopy
theory and thus introduced new invariants controlling
combinatorial complexity of maps and spaces, such as the
simplicial volume, which is responsible for degrees of maps
between manifolds. During the same period, Banach spaces and
probability theory underwent a geometric metamorphosis,
stimulated by the Levy?Milman concentration phenomenon,
encompassing the law of large numbers for metric spaces with
measures and dimensions going to infinity.
The first stages of the new developments were presented in
Gromov's course in Paris, which turned into the famous "Green
Book" by Lafontaine and Pansu (1979). The present English
translation of that work has been enriched and expanded with new
material to reflect recent progress. Additionally, four
appendices?by Gromov on Levy's inequality, by Pansu on "quasiconvex"
domains, by Katz on systoles of Riemannian manifolds, and by
Semmes overviewing analysis on metric spaces with measures?as
well as an extensive bibliography and index round out this unique
and beautiful book.
Table of contents
Preface to the French Edition.- Preface to the English Edition.-
Introduction: Metrics Everywhere.- Length Structures: Path Metric
Spaces.- Degree and Dilatation.- Metric Structures on Families of
Metric Spaces.- Convergence and Concentration of Metrics and
Measures.- Loewner Rediscovered.- Manifolds with Bounded Ricci
Curvature.- Isoperimetric Inequalities and Amenability.- Morse
Theory and Minimal Models.- Pinching and Collapse.- Appendix A:
"Quasiconvex" Domains in Rn.- Appendix B: Metric Spaces
and Mappings Seen at Many Scales.- Appendix C: Paul Levy's
Isoperimetric Inequality.- Appendix D: Systolically Free
Manifolds.- Bibliography.- Glossary of Notation.- Index.
Series: Modern Birkhauser Classics
Originally published as volume 86 in the series: Progress in
Mathematics
1st ed. 1990. 2nd printing, 2007, XX, 498 p., 13 illus.,
Softcover
ISBN: 978-0-8176-4566-3
About this book
The many diverse articles presented in these three volumes,
collected on the occasion of Alexander Grothendieck’s sixtieth
birthday and originally published in 1990, were offered as a
tribute to one of the world’s greatest living mathematicians.
Grothendieck changed the very way we think about many branches of
mathematics. Many of his ideas, revolutionary when introduced,
now seem so natural as to have been inevitable. Indeed, it is
difficult to fully grasp the influence his vast contributions to
modern mathematics have subsequently had on new generations of
mathematicians.
Many of the groundbreaking contributions in these volumes contain
material that is now considered foundational to the subject.
Topics addressed by these top-notch contributors match the
breadth of Grothendieck’s own interests, including: functional
analysis, algebraic geometry, algebraic topology, number theory,
representation theory, K-theory, category theory, and homological
algebra.
Table of contents
Foreword
Bibliographie d'Alexander Grothendieck
J. Dieudonne: De L'Analyse Fonctionnelle aux Fondements de la
Geometrie Algebrique
A.B. Altman and S.L. Kleiman: The Presentation Functor and the
Compactified Jacobian
M. Artin, J. Tate, and M. van den Bergh: Some Algebras Associated
to Automorphisms of Elliptic Curves
V. Balaji and C.S. Seshadri: Cohomology of a Moduli Space of
Vector Bundles
A. Beauville: Sur les Hypersurfaces dont les Sections Hyperplanes
sont a Module Constant
A.A. Beilenson, A.B. Goncharov, V.V. Schechtman, and A.N.
Varchenko: Aomoto Dilogarithms, Mixed Hodge Structures, and
Motivic cohomology of Pairs of Triangles on the Plane
P. Berthelot and W. Messing: Theorie de Dieudonne Cristalline III:
Theoremes d'Equivalence et de Pleine Fidelite
J.-M. Bismut, H. Gillet, and C. Soule: Complex Immersions and
Arakelov Geometry
S. Bloch and K. Kato: L-Functions and Tamagawa Numbers of Motives
L. Breen: Bitorseurs et Cohomologie Non Abelienne
J.-L. Brylinski: Non-commutative Ruelle-Sullivan Type Currents
Series: Modern Birkhauser Classics
Originally published as volume 87 in the series: Progress in
Mathematics
1st ed. 1990. 2nd printing, 2007, VIII, 564 p., 7 illus.,
Softcover
ISBN: 978-0-8176-4567-0
About this book
The many diverse articles presented in these three volumes,
collected on the occasion of Alexander Grothendieck’s sixtieth
birthday and originally published in 1990, were offered as a
tribute to one of the world’s greatest living mathematicians.
Grothendieck changed the very way we think about many branches of
mathematics. Many of his ideas, revolutionary when introduced,
now seem so natural as to have been inevitable. Indeed, it is
difficult to fully grasp the influence his vast contributions to
modern mathematics have subsequently had on new generations of
mathematicians.
Many of the groundbreaking contributions in these volumes contain
material that is now considered foundational to the subject.
Topics addressed by these top-notch contributors match the
breadth of Grothendieck’s own interests, including: functional
analysis, algebraic geometry, algebraic topology, number theory,
representation theory, K-theory, category theory, and homological
algebra.
Table of contents
P. Cartier et A. Voros: Une nouvelle interpretation de la formule
des traces de Selberg
C. Contou-Carrere: Jacobiennes generalisees globales relatives
P. Deligne: Categories tannakiennes
T. Ekedahl: On the Adic Formalism
G. Faltings: F-Isocrystals on Open Varieties: Results and
Conjectures
J.-M. Fontaine: Representations p-adiques des corps locaux
H.A. Hamm and Le D.T.: Rectified Homotopical Depth and
Grothendieck Conjectures
Y. Ihara: Automorphisms of Pure Sphere Braid Groups and Galois
Representations
L. Illusie: Ordinarite des intersections completes generales
M. Kashiwara: Kazhdan?Lusztig Conjecture for a Symmetrizable
Kac?Moody Lie Algebra
V.A. Kolyvagin: Euler Systems
R. Langlands and D. Shelstad: Descent for Transfer Factors
Series: Modern Birkhauser Classics
Originally published as volume 88 in the series: Progress in
Mathematics
1st ed. 1990. 2nd printing, 2007, VIII, 496 p., Softcover
ISBN: 978-0-8176-4568-7
About this book
The many diverse articles presented in these three volumes,
collected on the occasion of Alexander Grothendieck’s sixtieth
birthday and originally published in 1990, were offered as a
tribute to one of the world’s greatest living mathematicians.
Grothendieck changed the very way we think about many branches of
mathematics. Many of his ideas, revolutionary when introduced,
now seem so natural as to have been inevitable. Indeed, it is
difficult to fully grasp the influence his vast contributions to
modern mathematics have subsequently had on new generations of
mathematicians.
Many of the groundbreaking contributions in these volumes contain
material that is now considered foundational to the subject.
Topics addressed by these top-notch contributors match the
breadth of Grothendieck’s own interests, including: functional
analysis, algebraic geometry, algebraic topology, number theory,
representation theory, K-theory, category theory, and homological
algebra.
Table of contents
A. Lascoux: Anneau de Grothendieck de la variete de drapeaux
S. Lichtenbaum: New Results on Weight-Two Motivic Cohomology
G. Lusztig: Symmetric Spaces over a Finite Field
Z. Mebkhout: Le theoreme de positivite de l'irregularite pour les
Dx-modules
A. Ogus: The Convergent Topos in Characteristic p
A.N. Parshin: Finiteness Theorems and Hyperbolic Manifolds
M. Raynaud: p-groupes et reduction semi-stable des courbes
G.B. Shabat and V.A. Voevodsky: Drawing Curves Over Number Fields
L. Szpiro: Sur les proprietes numeriques du dualisant relatif
d'une surface arithmetique
R.W. Thomason and T. Trobaugh: Higher Algebraic K-Theory of
Schemes and of Derived Categories
A. Treibich et J.-L. Verdier (with an Appendix by J. Oesterle):
Solitons elliptiques
Yu.G. Zarhin: Linear Simple Lie Algebras and Ranks of Operators