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Stochastic Partial Differential Equations (SPDEs)

4th January 2010 to 2nd July 2010

Organisers: Professor Z Brzezniak (York), Professor M Hairer (Warwick), Professor M Röckner (Universität Bielefeld), Professor P Souganidis (Chicago) and Dr R Tribe (Warwick)

Programme Theme

Stochastic Partial Differential Equations are used to model many physical systems subjected to the influence of internal, external or environmental noise. They also arise when considering deterministic models from random initial conditions, or as tractable approximations to complex deterministic systems. In many cases the presence of noise leads to new phenomena with many recent examples in the physical sciences, biology and financial modelling.

The goal of the programme is to bring together the world leaders in Stochastic Partial Differential Equations working on various aspects of the theory, numerical approximations and applications, as well as in related scientific areas.

The following will be included as themes for the 6-month-long programme.

  • The study of classical problems (well-posedness, ergodicity, etc.): Kolmogorov equations, equations with constraints, analysis of operators on infinite dimensional spaces, control theory, stochastic viscosity solutions, equations with non-Gaussian or non time-decorrelated noise.
  • Applications: Stochastic models in fluid flow, stochastic nonlinear Schrödinger equation, stochastic Landau-Lifshitz equations, plasmas turbulence, stochastic porous media equations, branching diffusions, stochastic growth and disintegration models, interacting species models, epidemic modelling, financial modelling
  • Approximation methods: Numerical schemes (including finite element, splitting etc.), rates of convergence (theory and simulations), multiscale and asymptotic problems, particle approximations, perturbation problems.

Self-financing Participants

The Institute has some space available for participants who will not require financial assistance towards their subsistence, accommodation or travel costs. People who are interested in participating in the programme and who can find their own financial support are asked to contact the organisers by the end of January 2009. The researchers invited on that basis will be offered the use of the library, shared computer facilities and/or access to the wireless network, and help, if required, in finding accommodation.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons