Cantitate/Preț
Produs
Total produse
Vezi coșul
Optimal Transport de Cédric Villani

Optimal Transport: Grundlehren der mathematischen Wissenschaften, cartea 338

Autor Cédric Villani
en Limba Engleză Hardback – 30 sep 2008

Remarcăm în Optimal Transport o resursă monumentală care demonstrează aplicabilitatea practică a transportului optim în domenii diverse, de la ecuații cu derivate parțiale până la geometria metrică și probabilități. Lucrarea semnată de Cédric Villani nu este doar un tratat teoretic, ci un ghid riguros care transformă o problemă istorică, formulată inițial de Monge în secolul al XVIII-lea, într-un instrument modern de analiză. Reținem că această ediție de 1000 de pagini este concepută pentru a fi parcursă integral de către doctoranzi, oferind un aparat critic vast și o bibliografie comentată care facilitează navigarea prin literatura de specialitate. Structura volumului este organizată progresiv: primele secțiuni clarifică proprietățile de bază și dualitatea Kantorovich, în timp ce nucleul cărții explorează concepte precum interpolarea prin deplasare și curbura Ricci. În comparație cu Lectures on Optimal Transport de Luigi Ambrosio, care servește drept o introducere universitară concentrată, volumul de față oferă o acoperire enciclopedică, detaliind aspecte complexe de geometrie Riemanniană și „calcul Otto” pe care alte texte le tratează doar tangențial. De asemenea, Optimal Transport completează perspectiva oferită de Optimal Transport for Applied Mathematicians, adăugând o profunzime teoretică superioară în zona analizei funcționale și a inegalităților de concentrare. Poziționată în opera autorului între lucrări tehnice precum Nonlinear PDE’s and Applications și eseuri de reflecție asupra disciplinei precum Freedom in Mathematics, această monografie reprezintă pilonul central al contribuției lui Villani la matematica contemporană. Este o lucrare de referință care sintetizează tranziția de la teoria de bază la rezultatele de cercetare de ultimă oră, fiind esențială pentru orice bibliotecă de matematică avansată.

Citește tot Restrânge

Din seria Grundlehren der mathematischen Wissenschaften

  • 15% Quantitative Stochastic Homogenization and Large-Scale Regularity
    Preț: 57368 lei
  • 15% Loewner's Theorem on Monotone Matrix Functions
    Preț: 74096 lei
  • 20% Quantum Riemannian Geometry
    Preț: 63609 lei
  • 18% Regularity of Minimal Surfaces
    Preț: 100301 lei
  • 24% Lagerungen
    Preț: 84582 lei
  • 15% Basic Number Theory
    Preț: 47618 lei
  • 24% Minimal Surfaces
    Preț: 88425 lei
  • 24% Global Analysis of Minimal Surfaces
    Preț: 81209 lei
  • 15% Elementare Differentialgeometrie
    Preț: 43543 lei
  • Vorlesungen Über Differentialgeometrie I
    Preț: 34592 lei
  • Der Ricci-Kalkül
    Preț: 41022 lei
  • Der Ricci-Kalkül
    Preț: 44248 lei
  • 15% Praxis der Konformen Abbildung
    Preț: 43028 lei
  • 15% The Differential Geometry of Finsler Spaces
    Preț: 53087 lei
  • 15% Absolute Analysis
    Preț: 61043 lei
  • Absolute Analysis
    Preț: 34003 lei
  • 18% Markov Chains
    Preț: 73119 lei
  • Markov Chains with Stationary Transition Probabilities
    Preț: 37246 lei
  • 15% Die innere Geometrie der metrischen Räume
    Preț: 44113 lei
  • 15% Grundzüge der Mathematischen Logik
    Preț: 48461 lei
  • Topologische Lineare Räume I
    Preț: 45083 lei
  • Die Grundlagen der Theorie der Markoffschen Prozesse
    Preț: 33462 lei
  • Vorlesungen über Funktionentheorie
    Preț: 35165 lei
  • Equations Differentielles Operationnelles
    Preț: 47284 lei
  • 15% Vorlesungen Über Theoretische Mechanik
    Preț: 45065 lei
  • Hilbertsche Räume mit Kernfunktion
    Preț: 40662 lei
  • 18% Abstract Harmonic Analysis
    Preț: 74238 lei
  • Linear Partial Differential Operators
    Preț: 37319 lei
  • Einführung in die Theorie der Speziellen Funktionen der Mathematischen Physik
    Preț: 40616 lei
  • 15% The Theory of Branching Processes
    Preț: 55862 lei
  • Methoden der Mathematischen Physik
    Preț: 48286 lei
  • Funktionalanalysis und Numerische Mathematik
    Preț: 35002 lei
  • Markov Processes: Volume II
    Preț: 38910 lei
  • Einführung in die Wahrscheinlichkeitsrechnung und mathematische Statistik
    Preț: 40662 lei
  • 18% Quasiconformal Mappings in the Plane
    Preț: 72913 lei
  • Quasikonforme Abbildungen
    Preț: 45684 lei
  • Enumerability · Decidability Computability
    Preț: 38902 lei
  • Jordan-Algebren
    Preț: 34903 lei
  • Vorlesungen über Differenzenrechnung
    Preț: 50753 lei
  • Geometrische Ordnungen
    Preț: 41694 lei
  • 18% Endliche Gruppen I
    Preț: 77235 lei
  • Handbook for Automatic Computation
    Preț: 39395 lei
  • Handbook for Automatic Computation
    Preț: 39846 lei
  • 15% Stability of Motion
    Preț: 59595 lei
  • 15% Mathematische Hilfsmittel des Ingenieurs
    Preț: 45719 lei
  • 15% Elementarmathematik vom Höheren Standpunkte aus, I
    Preț: 44724 lei
  • 15% Mathematische Hilfsmittel des Ingenieurs
    Preț: 46752 lei

Preț: 93569 lei

Preț vechi: 114108 lei
-18%

Puncte Express: 1404
Paperback 98444 lei
Hardback 93569 lei

Carte indisponibilă temporar

Livrare prin curier în România Termenul estimat este afișat lângă disponibilitate.
Transport gratuit pentru acest produs Plată online sau ramburs, în funcție de opțiunile comenzii.
Retur gratuit în 14 zile Comandă securizată și suport în română.
 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9783540710493
ISBN-10: 3540710493
Pagini: 1000
Ilustrații: XXII, 976 p.
Dimensiuni: 160 x 241 x 59 mm
Greutate: 1.59 kg
Ediția:2009
Editura: Springer
Colecția Grundlehren der mathematischen Wissenschaften
Seria Grundlehren der mathematischen Wissenschaften

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

De ce să citești această carte

Această lucrare este indispensabilă cercetătorilor și studenților la doctorat care doresc să stăpânească fundamentele și aplicațiile moderne ale transportului optim. Cititorul câștigă o înțelegere profundă a legăturilor dintre geometrie și analiză, beneficiind de demonstrații complete și o bibliografie exhaustivă. Este singura resursă care acoperă spectrul total al domeniului, de la originile istorice la utilizarea transportului optim în studiul curburii Ricci.

Despre autor

Cédric Villani este unul dintre cei mai proeminenți matematicieni contemporani, distins cu Medalia Fields în anul 2010 pentru contribuțiile sale în domeniul amortizării Landau și al ecuației Boltzmann. Profesor la Universitatea din Lyon și fost director al Institutului Henri Poincaré, Villani este recunoscut pentru capacitatea sa de a face legături între fizica statistică și geometria diferențială. Opera sa variază de la tratate fundamentale de analiză matematică la lucrări interdisciplinare care explorează rolul inteligenței artificiale în medicină, reflectând o viziune globală asupra rolului matematicii în societatea modernă.

Descriere scurtă

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results.
PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
 

Cuprins

Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge—Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.

Recenzii

From the reviews:
"The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes." (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009)
“This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)
“The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)

Notă biografică

PIERRE CARTIER is academic by training, emeritus research director at the Centre national de la recherche scientifique (CNRS), and research scientist and a visitor (for indeterminate term) at the Institut des Hautes Etudes Scientifiques (IHES) of Bures-sur-Yvette. He is currently emeritus research director at the University Paris-Diderot. He is former member of the Bourbaki group. Born in 1932 in Sedan, Professor Carier, despite his provincial background, followed the path of excellence in his studies: a secondary school in his home town, followed by the lycée Saint-Louis in Paris and then the École normale superieure, and he obtained an advanced teaching degree and a doctorate in mathematics (1958). He also went to Princeton for two years; there he became acquainted with legendary figures such as Robert Oppenheimer and Andre Weil (brother of philosopher Simone Weil). Last but not least, he carried out a long military service in the marine corps against the backdrop ofthe Algerian war. He was then professor at the University of Strasbourg from 1961 to 1971. The years 1950-1975 were the hey-day of the Bourbaki group, of which he is one of the pillars; there he became friends with famous people like Cartan, Schwartz, Dieudonné, Chevalley, Weil, and with younger ones. A "mathematician without borders", Professor Cartier is active within the framework of the cooperation agency of the French Mathematical Society (Cimpa). He had been working in the Paris region since 1971, and he roamed around between Parisian academic institutions: University Paris-Sud, École polytechnique, École normale supérieure. He is not a member of the French Academy of Sciences (a voluntary choice). His scientific interests are quite diverse (even eclectic), but centered around group theory and mathematical physics. He often cited thesis relates to algebraic geometry, by he also contributed to differential geometry, number theory, combinatorics, numerical analysis, probability and mathematical physics. He wrote a reference book on Feynman Integrals (in collaboration with C. DeWitt-Morette, Functional Integration, Action and symmetries (Cambridge University Press, 2004). He is also one of the editors of Mathematics in the 21st Century: 6th World Conference, Lahore, March 2013 (Springer, 2014). He has supervised more than 40 doctoral theses, and he continues to work with some of my students on multiple zeta values and the Galois theory of differential equations. JEAN DHOMBRES is mathematician and historian of science, emeritus CNRS research director, director of studies at the Alexandre Koyre Centre of the École des hautes études en sciences sociales (EHESS), specialist of the mathematics of functional equations and of their applications, of epistemology of mathematics, and of the history of scientific communities and of the spread of scholarly ideas. Born in Paris in 1942, he studied at the École polytechnique and chose to take a chance with mathematical research instead of graduating as an engineer. He worked in functional analysis and through a series of encounters, he joined a small international group of scientists focused on functional equations. In fact it was in Bangkok that his first book was published as a result of a talk he had given at Chulalongkorn University in 1971. Besides many articles, he is happy to have been able to work with Janos Aczael, the uncontested leader in this field, having published with him a book on the subject, which has now become a reference, in Encyclopaedia of mathematics (University of Cambridge Press, republished in 2008). Probably as a reaction to his family background, as well as to a scientific training centered on France, he wished to see the world, by learning Chinese, by participating in the establishment of experimental classes in Wu Han in China, then by becoming scientific adviser in a French embassy for three years. He became professor at the University of Nantes as early as 1972. Since for a while he