# Prof. Massimiliano Gubinelli

Wallis Professor of Mathematics

Professorial Fellow at St. Anne's college

Head of the Stochastic Analysis Group

**Address**

Mathematical Institute

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

Euclidean field in two dimensions

*Gubinelli, M*

*Hofmanová, M*

*Rana, N*

*(19 May 2023)*

*http://arxiv.org/abs/2305.12017v1*

*Vecchi, F*

*Fresta, L*

*Gordina, M*

*Gubinelli, M*

*(15 May 2023)*

*http://arxiv.org/abs/2305.08497v1*

$d\geq 2$

*Cannizzaro, G*

*Gubinelli, M*

*Toninelli, F*

*(12 Apr 2023)*

*http://arxiv.org/abs/2304.05730v1*

subcritical regime

*Gubinelli, M*

*Rinaldi, P*

*(31 Mar 2023)*

*http://arxiv.org/abs/2303.18112v1*

QFT on the plane

*Vecchi, F*

*Gubinelli, M*

*Turra, M*

*(11 Dec 2022)*

*http://arxiv.org/abs/2212.05584v1*

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

Invited session speaker to the 2018 ICM in Rio.

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.

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

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.

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 Φ^{4}_{3} 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 Φ^{4}_{3}. *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