Videos

Introductory Workshop: Kinetic Theory & Stochastic Partial Differential Equations: Is there an applied side to rough PDEs?

Presenter
August 28, 2025
Keywords:
  • Interacting Particle Systems
  • many-body dynamics
  • Boltzmann equation
  • Vlasov equation
  • Lorentz gas
  • Schrödinger equation
  • singular SPDEs
  • stochastic quantization
  • regularity structures
  • paracontrolled distributions
MSC:
  • 82C40 - Kinetic theory of gases in time-dependent statistical mechanics
  • 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)
Abstract
In recent years rough paths theory has taken a very applied turn, primarily focusing on data analysis and machine learning. To the best of my knowledge, one cannot see (yet) this strong trend in rough PDEs or regularity structures. In this talk I will thus explore some avenues for the application of rough PDEs in various contexts. (Time permitting) I will cover control, finance, identification, and numerics for PDEs, reinforcement learning, and image processing. I will try to provide a broad picture, without entering in technical details.