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This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication. .

Algebraic geometry. --- Number theory. --- Algebraic Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry --- Geometry --- Vector bundles. --- Fiber spaces (Mathematics)

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Curves, Algebraic --- Fundamental groups (Mathematics)

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This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

Mathematics. --- Algebraic geometry. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Number theory. --- Probabilities. --- Global Analysis and Analysis on Manifolds. --- Algebraic Geometry. --- Probability Theory and Stochastic Processes. --- Number Theory. --- Geometry --- Mathematics --- Probabilities --- Control theory --- Math --- Science --- Global analysis. --- Geometry, algebraic. --- Distribution (Probability theory. --- Number study --- Numbers, Theory of --- Algebra --- Distribution functions --- Frequency distribution --- Characteristic functions --- Algebraic geometry --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

Number theory --- Algebraic geometry --- Differential geometry. Global analysis --- Geometry --- Operational research. Game theory --- Probability theory --- Mathematics --- landmeetkunde --- topologie (wiskunde) --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- wiskunde --- kansrekening --- getallenleer --- geometrie

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Mathematics