Prof. Massimiliano Gubinelli

PhD

Status

Academic Faculty

Wallis Professor of Mathematics

Professorial Fellow at St. Anne's college

Contact form

https://scholar.google.com/citations?user=D4PR4LYAAAAJ

+44 1865 615233

ORCID iD

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

Research groups

Stochastic Analysis

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

Recent publications

A singular integration by parts formula for the exponential Euclidean
QFT on the plane

Vecchi, F Gubinelli, M Turra, M (11 Dec 2022) http://arxiv.org/abs/2212.05584v1

A stochastic analysis of subcritical Euclidean fermionic field theories

Vecchi, F Fresta, L Gubinelli, M (26 Oct 2022) http://arxiv.org/abs/2210.15047v1

On the variational method for Euclidean quantum fields in infinite
volume

Barashkov, N Gubinelli, M (09 Dec 2021) http://arxiv.org/abs/2112.05562v2

Mixing for generic rough shear flows

Galeati, L Gubinelli, M (26 Jul 2021) http://arxiv.org/abs/2107.12115v1

Grassmannian stochastic analysis and the stochastic quantization of
Euclidean Fermions

Albeverio, S Borasi, L Vecchi, F Gubinelli, M (20 Apr 2020) http://arxiv.org/abs/2004.09637v4

Teaching

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

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.

Prizes, awards, and scholarships

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

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.

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