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 Astérisque 2009; 420 pp; softcover Number: 327 ISBN-10: 2-85629-288-7 ISBN-13: 978-2-85629-288-4 List Price: US$135 Member Price: US$108 Order Code: AST/327 See also: From Probability to Geometry (II): Volume in Honor of the 60th Birthday of Jean-Michel Bismut - Xianzhe Dai, Remi Leandre, Xiaonan Ma and Weiping Zhang This is the first of two volumes that contain original research articles submitted by colleagues and friends to celebrate the 60th birthday of Jean-Michel Bismut. These articles cover a wide range of subjects in probability theory, global analysis, and arithmetic geometry to which Jean-Michel Bismut has made fundamental contributions. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in geometry. Table of Contents S. Aida -- Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space: I. Unbounded one particle Hamiltonians S. Albeverio and S. Mazzucchi -- Infinite dimensional oscillatory integrals with polynomial phase function and the trace formula for the heat semigroup R. F. Bass and E. Perkins -- A new technique for proving uniqueness for martingale problems M. Grothaus, L. Streit, and A. Vogel -- Feynman integrals as Hida distributions: the case of non-perturbative potentials H. Kunita -- Smooth density of canonical stochastic differential equations with jumps J. R. Norris -- Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space I. Shigekawa -- Witten Laplacian on a lattice spin system A. Alekseev, H. Bursztyn, and E. Meinrenken -- Pure spinors on Lie groups M.-T. Benameur and P. Piazza -- Index, eta and rho invariants on foliated bundles A. Berthomieu -- Direct image for some secondary $$K$$-theories J.-B. Bost and K. Künnemann -- Hermitian vector bundles and extension groups on arithmetic schemes II. The arithmetic Atiyah extension