Videos

Introductory Workshop: Kinetic Theory & Stochastic Partial Differential Equations: Stochastic heat flow: axiomatic formulation and applications

Presenter
August 25, 2025
SLMath
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)
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Abstract
The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation, specifically at the critical dimension of two and near the critical temperature. In this talk, I will present recent work on an axiomatic formulation and construction of the SHF based on its moments, and discuss how this formulation can be applied to solve a range of problems.