Prof. Massimiliano Gubinelli

PhD

Status

Academic Faculty

Wallis Professor of Mathematics

Professorial Fellow at St. Anne's college

Head of the Stochastic Analysis Group

+44 1865 615233

Contact form

https://mgubi.github.io

ORCID iD

https://orcid.org/0000-0002-4014-2949

Research groups

Address

Room S1.42

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

with H. Koch and T. Oh. Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity. Journal European Mathematical Society, 2022. To appear. arXiv:1811.07808

with M. Hofmanová. A PDE Construction of the Euclidean Φ⁴₃ Quantum Field Theory. Communications in Mathematical Physics, 2021. 10.1007/s00220-021-04022-0

with L. Galeati. Noiseless regularisation by noise. Revista Matemática Iberoamericana, 2021. 10.4171/RMI/1280

with N. Perkowski. The infinitesimal generator of the stochastic Burgers equation. Probability Theory and Related Fields, 2020. 10.1007/s00440-020-00996-5

with N. Barashkov. A variational method for Φ⁴₃. Duke Mathematical Journal, 169(17):3339–3415, 2020. 10.1215/00127094-2020-0029

with P. Imkeller and N. Perkowski. Paracontrolled distributions and singular PDEs. Forum of Mathematics. Pi, 3:0, 2015. 10.1017/fmp.2015.2

with F. Flandoli and E. Priola. Well-posedness of the transport equation by stochastic perturbation. Inventiones Mathematicae, 180(1):1–53, 2010. 10.1007/s00222-009-0224-4

Ramification of rough paths. Journal of Differential Equations, 248(4):693–721, 2010. 10.1016/j.jde.2009.11.015

Controlling rough paths. Journal of Functional Analysis, 216(1):86–140, 2004. 10.1016/j.jfa.2004.01.002

Teaching

C8.1 Stochastic Differential Equations (MT22) [url]

Further details

I'm interested in computer languages and software development. I'm one of the lead developers of TeXmacs, a free scientific editing platform designed to create beautiful technical documents.

Recent publications

A simple construction of the sine‐Gordon model via stochastic quantization

Gubinelli, M Hairer, M Oh, T Zine, Y Journal of the London Mathematical Society volume 112 issue 1 (25 Jun 2025)

Nonlinear PDEs with modulated dispersion IV: normal form approach and
unconditional uniqueness

Gubinelli, M Li, G Li, J Oh, T (30 May 2025) http://arxiv.org/abs/2505.24270v1

Non-commutative L p spaces and Grassmann stochastic analysis

De Vecchi, F Fresta, L Gordina, M Gubinelli, M Probability Theory and Related Fields volume 192 issue 3-4 949-1029 (25 May 2025)

A stochastic analysis of subcritical Euclidean fermionic field theories

De Vecchi, F Fresta, L Gubinelli, M The Annals of Probability volume 53 issue 3 (01 May 2025)

Stochastic Quantisation

Gubinelli, M Encyclopedia of Mathematical Physics 648-667 (2025)

Prizes, awards, and scholarships

Junior member of the Institut Universitaire de France (2013-2018)

Invited session speaker to the 2018 ICM in Rio.

Research interests

My current main area of research is stochastic analysis in particular in connection with problems of constructive quantum field theory. The main focus is to develop tools and concepts which are suitable to describe and analyse the pathwise behaviour of quantum or random fields, including their description via partial differential equations and renormalization group ideas. More broadly speaking I'm interested in problems of statistical mechanics of multiscale systems, analysis of PDEs with random terms and homogenisation theory, mathematical quantum mechanics, path-integral formalisms, non-commutative probability and non-commutative geometry. I've also some side interests in formalisation of mathematics.