Series:De Gruyter Studies in Mathematics 48
24 x 17 cmApprox. x, 350 pages
Language: English
Type of Publication: Monograph
Keywords:
Denumerable Structures; Dirichlet Spaces; Second-order Parabolic Equations; Probabilistic Potential Theory; Diffusion Processes
This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and their associated Markov processes are important and powerful tools in the theory of Markov processes and their applications. The theory is well studied and used in various fields. In this monograph, we intend to generalize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization, we can cover the wide class of Markov processes and analytic theory which do not possess the dual Markov processes. In particular, under the semi-Dirichlet form setting, the stochastic calculus is not well established yet. In this monograph, we intend to give an introduction to such calculus. Furthermore, basic examples different from the symmetric cases are given. The text is written for graduate students, but also researchers.
Series:De Gruyter Studies in Mathematics 54
24 x 17 cmApprox. x, 350 pages
Language: English
Type of Publication: Monograph
This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps".
The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener?Poisson space. Solving the Hamilton?Jacobi?Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory.
The field of jump processes is nowadays quite wide-ranging, from the Levy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph.
Seminaires et Congres 22 (2011), xviii+174 pages
Presentation
Extremals for Hardy-Sobolev type inequalities: the influence of the curvature
Frederic Robert
Seminaires et Congres 22 (2011), 1-15
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On the Kahler classes of constant scalar curvature metrics on blow ups
Claudio Arezzo, Frank Pacard
Seminaires et Congres 22 (2011), 17-29
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Fully nonlinear equations, ellipticity, and curvature pinching
Matthew J. Gursky
Seminaires et Congres 22 (2011), 31-45
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Visualization of the eigenvalue problems of the Laplacian for embedded surfaces and its applications
Masaki Jumonji, Hajime Urakawa
Seminaires et Congres 22 (2011), 47-91
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The role of integrability by compensation in conformal geometric analysis
Tristan Riviere
Seminaires et Congres 22 (2011), 93-127
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Mean curvature flow solitons
Norbert Ernst Hungerbuhler, Beatrice Roost
Seminaires et Congres 22 (2011), 129-158
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Self-similar expanding solutions for the planar network flow
Rafe Mazzeo, Mariel Saez
Seminaires et Congres 22 (2011), 159-173
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Memoires de la SMF 129 (2012), vi + 99 pages
Acheter l'ouvrage
Soit un corps algebriquement clos de caracteristique zero et soit un anneau de polynomes de Laurent en deux variables sur . La motivation principale derriere ce travail est une classe d'algebres de Lie de dimension infinie sur , appelees extended affine Lie algebras (EALAs). Ces algebres correspondent a des torseurs sous des groupes algebriques lineaires sur . Dans ce travail nous classifions les -torseurs sous les groupes classiques de rang assez grand pour les types exterieur, et pour le type interieur sous des hypotheses plus fortes. Ainsi, nous pouvons deduire des resultats sur des EALAs. Nous obtenons aussi une reponse affirmative a une variante de la conjecture II de Serre pour l'anneau : tout -torseur lisse sous un groupe semi-simple simplement connexe de rang assez grand de type classique , et est trivial.
Mots-clefs : Algebre de Lie de dimension infinie, EALA, anneau de polynomes de Laurent, cohomologie galoisienne, groupe algebrique lineaire classique, algebre d'Azumaya a involution, forme hermitienne, theorie de Witt triangulaire
Infinite Dimensional Lie Algebras and Descent Theory
Let be an algebraically closed field of characteristic zero and let be the Laurent polynomial ring in two variables over . The main motivation behind this work is a class of infinite dimensional Lie algebras over , called extended affine Lie algebras (EALAs). These algebras correspond to torsors under algebraic groups over . In this work we classify -torsors under classical groups of large enough rank for outer type and types , as well as for inner type under stronger hypotheses. We can thus deduce results on EALAs. We also obtain a positive answer to a variant of Serre's Conjecture II for the ring : every smooth -torsor under a semi-simple simply connected -group of large enough rank of classical type is trivial.
Keywords: Infinite Dimensional Lie Algebra, Extended Affine Lie Algebra (EALA), Laurent Polynomial Ring, Galois Cohomology, Classical Linear Algebraic Group, Azumaya Algebra with Involution, Hermitian Form, Triangular Witt Theory
ISBN : 978-2-85629-349-2
ISSN : 0249-633-X
Publie avec le concours de : Centre National de la Recherche Scientifique
Asterisque 346 (2012), XI + 318 pages
Acheter l'ouvrage
Presentation
Symplectic local Root numbers, central critical L. Values and restriction problems in the representation theory of classical groups
Wee Teck Gan, Benedict H. Gross and Dipendra Prasad
Asterisque 346 (2012)
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Restrictions of representations of Classical groups : examples
Wee Teck Gan, Benedict H. Gross and Dipendra Prasad
Asterisque 346 (2012)
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Une formule integrale reliee a la conjecture locale de Gross-Prasad, 2e partie : Extension aux representations temperees
Jean-Loup Waldspurger
Asterisque 346 (2012)
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Une variante dfun resultat de Aizenbud, Gourevitch, Rallis et Schiffman
Jean-Loup Waldspurger
Asterisque 346 (2012)
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Asterisque 348 (2012), x+496 pages
Acheter l'ouvrage
Resume :
Comme les precedents volumes de ce seminaire, qui compte maintenant plus de mille exposes, celui-ci contient seize exposes de synthese sur des sujets d'actualite : trois situes entre analyse et geometrie, trois de geometrie algebrique, deux de geometrie diophantienne, deux lies au programme de Langlands, deux en theorie des groupes, un de topologie algebrique, un sur le modele d'Ising et deux en physique mathematique.
Mots-clefs : , algebres de von Neumann, analyse complexe discrete, asymetrie, asymptotique, champs, cohomologie completee, compatibilite local-global, conjecture d'Andre-Oort, conjecture de Bogomolov, conjecture de Serre II, conjecture de Zilber-Pink, connexite rationnelle, corps convexes, courbes pseudo-holomorphes, creusage spectral, decomposition de John approchee, Determinant jacobien, diffusion, espaces de Sobolev, equation de Schrodinger nonlineaire, equations aux derivees partielles, equirepartition, existence, fibration de Hitchin, fonction modulaire, fonctions BV, formule des traces, geometrie algebrique reelle, geometrie symplectique reelle, graphes expanseurs, groupes d'homotopie stable, Groupes non-moyennables, hauteurs, inegalite de Sobolev a trace, intersections exceptionnelles, invariance conforme, invariant de Kervaire, invariants de Gromov-Witten, inversibilite restreinte, lemme fondamental, mecanique des fluides, methodes de crible, modele d'Ising, multiplication complexe, obstruction de Brauer, percolation, physique statistique, points speciaux, probleme de Lehmer, problemes enumeratifs, propriet'e (tau), reduction dimensionnelle, relations d'equivalence mesurees, spectres en anneaux structures, surfaces K3, theoreme de Torelli global, theorie de l'homotopie chromatique, theorie de l'homotopie stable equivariante, theorie du controle, theorie symplectique des champs, theories o-minimales, transport de Brenier, varietes de Shimura, Varietes hyperkahleriennes, varietes semi-abeliennes
Bourbaki Seminar, volume 2010/2011, talks 1027-1042
As in the preceding volumes of this seminar, which now counts more than one thousand talks, one finds here sixteen survey lectures on topics of current interest : three lectures between analysis and geometry, three about algebraic geometry, three on diophantine geometry, two related to Langlands' program, two about group theory, one on algebraic topology, one related to Ising's model, and two about mathematical physics.
Keywords: , Andre-Oort conjecture, anomalous intersections, approximate John decomposition, asymmetry, asymptotics, Bogomolov conjecture, Brauer obstructions, Brenier transport, BV functions, chromatic homotopy theory, completed cohomology, complex multiplication, conformal invariance, conjecture of Zilber-Pink, control theory, convex bodies, dimensionality reduction, discrete complex analysis, enumerative problems, equidistribution, equivariant stable homotopy theory, existence, expander graphs, fluid mechanics, fundamental lemma, global Torelli theorem, Gromov-Witten invariants, heights, Hitchin fibration, hyperkahler manifolds, Ising model, Jacobian determinant, K3 surfaces, Kervaire invariant, Langlands program, Lehmer's problem, local-global compatibility, measured equivalence relations, modular function, nonamenable groups, nonlinear Schrodinger equation, o-minimal theories, partial differential equations, percolation, property (tau), pseudo-holomorphic curves, rational connectedness, real algebraic geometry, real symplectic geometry, restricted invertibility, scattering, semiabelian varieties, Serre's conjecture II, Shimura varieties, sieve methods, Sobolev spaces, special points, spectral sparsification, stable homotopy groups, stacks, statistical physics, structured ring spectra, symplectic field theory, trace formula, trace Sobolev inequality, von Neumann algebras
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ISBN : 978-2-85629-351-5
ISSN : 0303-1179
Publie avec le concours de : Centre National de la Recherche Scientifique