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Quantum and stochastic mathematical physics. Sergio Albeverio, adventures of a mathematician, Verona, Italy, March 25–29, 2019. (English) Zbl 1515.81020

Springer Proceedings in Mathematics & Statistics 377. Cham: Springer (ISBN 978-3-031-14030-3/hbk; 978-3-031-14033-4/pbk; 978-3-031-14031-0/ebook). xviii, 385 p. (2023).

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Publisher’s description: Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and \(p\)-adic numbers.
The articles of this volume will be reviewed individually.
Indexed articles:
Da Prato, Giuseppe; Tubaro, Luciano, Wick powers in stochastic PDEs: an introduction, 1-15 [Zbl 07819342]
Guerra, Francesco, The Albeverio-Høegh-Krohn paradox in Nelson stochastic mechanics, 17-28 [Zbl 07819343]
Streit, Ludwig, Energy forms and quantum dynamics, 29-39 [Zbl 07819344]
Cipriani, Fabio E. G., The emergence of noncommutative potential theory, 41-106 [Zbl 07819345]
Dell’Antonio, Gianfausto, Contact interactions and gamma convergence, 107-125 [Zbl 07819346]
Figari, Rodolfo; Teta, Alessandro, On the Hamiltonian for three bosons with point interactions, 127-145 [Zbl 07819347]
Mazzucchi, Sonia, Mathematical theory of Feynman path integrals, 147-171 [Zbl 07819348]
Sengupta, Ambar N., Gauge theories in low dimensions: reminiscences of work with Sergio Albeverio, 173-185 [Zbl 07819349]
Lindstrøm, Tom, The allure of infinitesimals: Sergio Albeverio and nonstandard analysis, 187-215 [Zbl 07819350]
Daletskii, Alexei; Kondratiev, Yuri; Pasurek, Tanja, Sergio’s work in statistical mechanics: from quantum particles to geometric stochastic analysis, 217-246 [Zbl 07819351]
Ferrario, Benedetta; Flandoli, Franco, Hydrodynamic models, 247-268 [Zbl 07819352]
Brzeźniak, Zdzisław; Deugoué, Gabriel; Razafimandimby, Paul André, On strong solution to the 2D stochastic Ericksen-Leslie system: a Ginzburg-Landau approximation approach, 269-293 [Zbl 07819353]
Mandrekar, V.; Rüdiger, B., Stability properties of mild solutions of SPDEs related to pseudo differential equations, 295-313 [Zbl 07819354]
Karwowski, Witold, Random processes on non-Archimedean spaces, 315-342 [Zbl 1534.60113]

MSC:

81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
00B25 Proceedings of conferences of miscellaneous specific interest

Biographic References:

Albeverio, Sergio
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