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Recent Trends in Stochastic Partial Differential Equations: Recent developments on random data theory for dispersive PDEs

Presenter
November 20, 2025
SLMath
Keywords:
  • stochastic partial differential equations
  • regularity structures
  • paracontrolled calculus
  • nonlinear dispersive equations
  • Gibbs measures
  • homogenization
  • stochastic fluid dynamics
  • quantum field theory
MSC:
  • 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)
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Abstract
We review recent works on the random data theory for dispersive equations, including almost sure local well-posedness, invariance of Gibbs measures, and wave kinetic theory. We will cover several results collaborated with various people, including B. Bringmann, Z. Hani, A. Nahmod and H. Yue.