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This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.

Potential theory (Mathematics) --- Markov processes. --- Semigroups. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Group theory --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Global analysis. --- Quantum theory. --- Global differential geometry. --- Potential theory (Mathematics). --- Global Analysis and Analysis on Manifolds. --- Quantum Physics. --- Quantum Information Technology, Spintronics. --- Differential Geometry. --- Potential Theory. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Thermodynamics --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Quantum physics. --- Quantum computers. --- Spintronics. --- Differential geometry. --- Differential geometry --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Topology --- Greifswald <2007>

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This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Algebraic geometry --- Differential geometry. Global analysis --- Operator theory --- Functional analysis --- Mathematics --- analyse (wiskunde) --- differentiaal geometrie --- functies (wiskunde) --- statistiek --- wiskunde --- geometrie

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Differential geometry. Global analysis --- Differential equations --- Computer. Automation --- computergestuurd meten --- differentiaalvergelijkingen --- Laplacetransformatie --- differentiaal geometrie