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 fieldtheory. 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.
Mục lục
Drawing by Solveig Albeverio.- Introduction.- Chapter 1. G. Da Prato and L. Tubaro, Wick Powers in stochastic PDE’s: an introduction.- Chapter 2. F. Guerra, The Albeverio-Hoegh-Krohn paradox in Nelson stochastic mechanics.- Chapter 3. Ludwig Streit: Energy Forms and Quantum Dynamics.- Chapter 4. F. Cipriani, The emergence of non-commutative potential theory.- Chapter 5. G. Dell’Antonio, Contact interactions and Gamma convergence.- Chapter 6. R. Figari and A. Teta, On the Hamiltonian for three bosons with point interactions.- Chapter 7. S. Mazzucchi, Mathematical theory of Feynman path integrals.- Chapter 8. A. Sengupta, Gauge theories in low dimensions: reminiscences of work with Sergio Albeverio.- Chapter 9. T. Lindstrom, The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis.- Chapter 10. A. Daletskii and Y. Kondratiev, Sergio’s work in statistical mechanics: from quantum particles to geometric stochastic analysis.- Chapter 11. B. Ferrario and F. Flandoli: Hydrodynamic models.- Chapter 12. Z. Brzezniak, G. Deugoué and P. André Razafimandimby, On strong solution to the 2d stochastic Ericksen-Leslie system: a Ginzburg-Landau approximation approach.- Chapter 13. V. Mandrekar and B. Rüdiger: Stability properties of mild solutions of SPDEs related to Pseudo Differential Equations.- Chapter 14. Witold Karwowski: Random Processes on non-Archimedean spaces.- Interview with Sergio Albeverio.- Interview with Colleagues and Friends of Sergio Albeverio.- Homage by Philippe Blanchard.- CV and Publications by Sergio Albeverio.- Acknowledgements.- Photos selected by Sergio Albeverio.
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