Stochastic Partial Differential Equations

Stochastic partial differential equations arise naturally in several models of random phenomena, in such fields as biology, physics, and engineering. In particular, while deterministic models represent an efficient tool to describe time-evolution of real-world systems, they fail in rendering the presence of possible microscopic uncertainty of the model. Such randomness components may be related to several factors (such as temperature oscillations or magnetic/configurational perturbations) and are usually tracked through the introduction of a stochastic source of randomness in the equations involved.

One of the most challenging goals of the mathematics of stochastic partial differential equations is the understanding of quantitative and qualitative properties of solutions and their dependence on the coefficients. The complexity of such a topic requires a wide variety of mathematical techniques, bridging from functional analysis to probability, from monotone and convex analysis to optimization theory, from stochastic modelling to numerics.

The great relevance for applications and the enormous range of theoretical tools involved have contributed to an amazing development of this field in the last years. However, several aspects are still open in many directions. One of the main goals of this workshop is to bring together researchers interested in the mathematics of SPDEs in order to tackle the most recent advances of the theory and possibly create an international environment for cross-fertilization of ideas. Topics that will be addressed in the workshop include:

  • Nonlinear stochastic partial differential equations
    • Existence, uniqueness, regularity, and dependence on the data
    • Abstract variational and monotonicity techniques, concepts of solution
    • Long-time behaviour, ergodicity properties and Kolmogorov equations
    • Numerical approximation
  • Stochastic optimal control
    • Stochastic maximum principle, first order conditions for optimality
    • Backward stochastic (partial) differential equations
    • Adjoint system and duality techniques
  • Stochastic modelling
    • Stochastic phase-field models in physics and biology
    • Stochastic fluid dynamics
    • Upscaling from discrete to continuum, analysis and simulations

Coming soon.

There is currently no participant information available for this event.
At a glance
March 7, 2022 — March 11, 2022
ESI Boltzmann Lecture Hall
Sandra Cerrai (U of Maryland)
Martin Hairer (Imperial College, London)
Carlo Marinelli (IRIS)
Eulalia Nualart (UPF)
Luca Scarpa (U Vienna)
Ulisse Stefanelli (U Vienna)