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.
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.
