Scientists / Open questions
Martin Hairer
Stochastic analysis; stochastic partial differential equations
2014 Fields Medal
7 questions
An elementary construction of the renormalised generalised parabolic Anderson model in dimension two and of the parabolic Anderson model in dimension three
Quantitative homogenisation of stochastic PDEs with multiscale structure: Hilbert-Schmidt noise, convergence rates, and the integer-cell assumption
Critical and supercritical singular stochastic PDEs and the short-range critical Glauber conjecture: the surviving open core of the theory of regularity structures
Large-scale limits of 3D continuous phase coexistence models beyond Gaussian noise and polynomial potentials: the unresolved cases of the Hairer-Xu classification
Higher-order expansion for fluctuations around the homogenised semilinear random PDE of Hairer–Pardoux
Open design and analysis problems for Ticketed Diffusion Monte Carlo: optimal biasing potential, population-control bias, finite-step error bounds, and branching schedules
Convergence of ticketed diffusion Monte Carlo to its continuous-time branching limit beyond the one-dimensional linear-potential toy model (the Brownian fan)