What's new

10 November 2026 ⋅ preprint
Composite local observables of sine-Gordon via stochastic analysis

With P. Paulovics (arXiv:2611.14296). A nonperturbative construction of local composite observables of the sine-Gordon model on the full plane up to \(\beta^2 < 6 \pi\), including vertex fields in the optimal Wick regime and derivatives of any order, combining renormalisation group ideas with stochastic analysis.

10 November 2026 ⋅ writing
Observables beyond the real line

The second post of the series on observables and self-adjoint operators: joint observables of commuting operators, normal operators and observables with values in manifolds, states as sources of probability laws, and what extra structure geometry and quantization require. A companion page gives the proofs and complements.

5 November 2026 ⋅ paper
Nonlinear PDEs with modulated dispersion II: Korteweg–de Vries equation

With K. Chouk, G. Li, J. Li and T. Oh, accepted for publication in the Memoirs of the European Mathematical Society (arXiv:1406.7675). See the publications page.

5 November 2026 ⋅ lectures
A constructive introduction to quantum field theory

Notes and slides (PDF, HTML and TeXmacs sources) of my course at SISSA, Trieste, 20 October–9 November 2026. Lectures 1–5 have been delivered. The provisional materials for Lectures 6–7 give an FBSDE construction of \(\phi^4_3\) on the torus, with new results from joint work with Sarah-Jean Meyer. Course page added 21 October 2026; updated 5 November 2026.

30 October 2026 ⋅ lectures
A stochastic analysis perspective on Euclidean fields

Lecture notes and the eight recordings of my course at the 53rd Saint-Flour Probability Summer School (2025), with timestamps linking to each topic. The teaching page now also lists my lecture series.

27 October 2026 ⋅ talk
Stochastic observables and the forward–backward flow of a Euclidean field

Workshop Deterministic and Stochastic Evolution Equations, Scuola Normale Superiore, Pisa (slides). The presentations archive also has new slides from the SISSA workshop (September 28–October 2, 2026) and from York (March 11, 2026).

23 October 2026 ⋅ writing
What do we talk about when we talk about unbounded self-adjoint operators?

The first post of a series that uses the notion of an observable as an organising principle for the theory of unbounded self-adjoint operators: spectral measures, resolvents, unitary groups and strong resolvent convergence. A companion page gives the proofs and complements.

12 October 2026 ⋅ paper
Parabolic stochastic quantisation of the fractional \(\Phi^4_3\) model in the full subcritical regime

With P. Duch and P. Rinaldi, published online in the Journal of the European Mathematical Society (arXiv:2303.18112).

September 2026 ⋅ paper
Constructive stochastic quantisation

My lecture notes from the CIME school “Statistical Mechanics and Stochastic PDEs” (Cetraro, 2023), forthcoming in Springer's Lecture Notes in Mathematics, vol. 2401.

2 September 2026 ⋅ talk
Stochastic observables and constructive RG

Invited plenary talk at the 13th International Conference on the Exact Renormalization Group (ERG2026), University of Sussex, Brighton (slides).

July 2026 ⋅ papers
Nonlinear PDEs with modulated dispersion

Part IV, Normal form approach and unconditional uniqueness (with G. Li, J. Li and T. Oh), published in the Peking Mathematical Journal. Two new preprints: Part III, Multiplicative noises (with A. Chapouto, G. Li, J. Li and T. Oh, arXiv:2607.08385), and Refined global well-posedness for the periodic modulated Korteweg–de Vries equation (with D. Greco, S. Liu and T. Oh, arXiv:2607.09023).

January 2026 ⋅ preprint
On the weak coupling limit of the periodic quantum Lorentz gas

With V. Sanjay (arXiv:2601.07453).