(Last updated in 2024; includes corrections of some typos in the published versions.) A full copy of the monograph. This complements existing works on the theory of rough paths. The pdf file available on this page is purely for personal use and cannot be sold, modified, or redistributed.
(Last updated in 2014.) Notes from lecture series in Rennes, Bonn, Mambucaba, and ETH Zurich, giving a concise overview of regularity structures.
(Last updated in 2025.) A postgraduate-level survey of techniques and results in stochastic PDEs, beginning with Gaussian measures and semigroup theory before moving to nonlinear equations.
(Last updated in 2026.) Lecture notes from Masters-level courses taught at the University of Warwick, Imperial College London, and EPFL, including Gaussian measure theory, Malliavin calculus, Hörmander's theorem, Nelson's construction of the Φ42 Euclidean quantum field theory, and the Nualart-Peccati fourth moment theorem.
(Last updated in 2021.) Notes for a minicourse on long-time behaviour of Markov processes, including convergence rates, subgeometric convergence, and a probabilistic proof of Hörmander's theorem.
(Last updated in 2007.) Lecture notes from an LMS minicourse at Imperial College London on spectral properties of hypoelliptic Schrodinger-type operators.
(Last updated in 2008.) Lecture notes from an LMS minicourse at Imperial College London on the ergodic theory of stochastic PDEs.
(Last updated in 2018.) A fourth-year course on the long-time behaviour of Markov processes, Perron-Frobenius theory, generalized laws of large numbers, and constructive convergence techniques.