Stochastic Analysis, Stochastic Partial Differential Equations and Applications to Fluid Dynamics and Particle Systems
Partially supported by INDAM
1 March 2006 - 31 July 2006Aims
The activities of the semester will include some lecture courses of different length, shorter series of lectures, and a few workshops or very intensive weeks.
The semester is aimed at giving the opportunity to young researchers to learn advanced topics and to allow experts to meet and discuss the frontiers of the subjects.
Research Directions
The main topics addressed in the semester will be:
Stochastic analysis in infinite dimensions Stochastic partial differential equations Dirichlet forms and Kolmogorov equations Particle systems and statistical mechanics Stochastic fluid dynamics
Infinite dimensional analysis, using probabilistic tools, is a rich modern subject covering Dirichlet forms, parabolic and elliptic equations in Hilbert spaces, Malliavin calculus and other topics. Infinite dimensional diffusions expecially in the form of Stochastic PDE's represent an expanding area of research. They arise very often in modelling the macroscopic fluctuations of microscopic systems. Systems of interacting particles evolving according to a stochastic dynamics have been recently a main source of inspiration in the study of irreversible phenomena in non equilibrium statistical mechanics. Statistical hydrodynamics is a leading subject in the study of turbulence.
Workshops
- Random Dynamical Systems in Infinite Dimensions, March 28-29, 2006
- Stochastic Partial Differential Equations, April 3-8, 2006 Local Committee: Sandra Cerrai (Università di Firenze), Lorenzo Zambotti (Politecnico di Milano ), Luciano Tubaro (Università di Trento)
- Hydrodynamic limits and Particle Systems, June 5-10, 2006 Local Committee: Lorenzo Bertini (Università di Roma 'La Sapienza'), Marco Isopi (Università di Roma 'La Sapienza'), Lorenzo Zambotti (Politecnico di Milano )
- Stochastic Fluid Mechanics and SPDEs, July 24-28, 2006 Local Committee: Massimiliano Gubinelli (Università di Pisa), Marco Romito (Università di Firenze)
Moreover, the following series of lectures are planned:
Markov processes and stochastic equations (April, J. Zabczyk) Elements of Ergodic Theory for SPDE's (May, B. Goldys) Central limit theorems for Markov processes (May-June, C. Landim) Introduction to the theory of Spin glasses (June-July, F. Guerra) Introduction to SPDEs (June-July, A. Debussche) Random walk in random environment (July, E. Bolthausen)