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This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- Geometric quantization. --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Geometry, Differential --- Quantum theory --- Differential equations, partial. --- Global differential geometry. --- Global analysis. --- Partial Differential Equations. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Mathematical Physics. --- Partial differential equations --- Partial differential equations. --- Differential geometry. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical physics. --- Physical mathematics --- Physics --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential geometry

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Boundary value problems --- Differential operators

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This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Algebraic geometry --- Differential geometry. Global analysis --- Partial differential equations --- Mathematics --- Mathematical physics --- differentiaalvergelijkingen --- differentiaal geometrie --- statistiek --- wiskunde --- fysica --- geometrie

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This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Probabilities. --- Quantum field theory. --- String theory. --- Functional analysis. --- Operator theory. --- Probability Theory and Stochastic Processes. --- Quantum Field Theories, String Theory. --- Functional Analysis. --- Operator Theory.

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This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Probabilities. --- Quantum field theory. --- String theory. --- Functional analysis. --- Operator theory. --- Probability Theory and Stochastic Processes. --- Quantum Field Theories, String Theory. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk