

1998  Diploma in Physics, University of Pisa, Italy  2001  2006  Ricercatore (Assistant Professor), Institute of Applied Mathematics, University of Pisa, Italy  2003  PhD in Theoretical Physics, University of Pisa, Italy  2006  2008  Maître de conférences, ParisSud University, Orsay, France  2008  2011  Professeur des Universités (2ème classe), Paris Dauphine University, Paris, France  2011  2015  Professeur des Universités (1ère classe), Paris Dauphine University, Paris, France  2012  2015  Parttime Professor, École Polytechnique, Palaiseau, France  Since 2015  Hausdorff Chair (W3), University of Bonn 


I’m interested in problems of mathematical physics in connection with stochastic analysis. More generally in the description and analysis of random influences in evolutionary systems inspired by physics. In recent years I’ve been working in developing Rough Path Theory, which is a set of ideas and tools which allows a detailed analysis of irregular signals on nonlinear systems. I’ve generalised the original theory, introduced by T. Lyons, to a wider class of signals, Branched Rough Paths and proposed various other theories in order to handle more complex dynamics like those underlying parabolic and hyperbolic PDEs. Rough paths and their generalisations have inspired the theory of Regularity Structures, invented by Hairer to describe the local structure of solutions to singular PDEs of the kind appearing in mathematical physics: the Stochastic Quantisation Equation, the Kardar—Parisi—Zhang equation, the parabolic Anderson model. In a parallel development, in collaboration with Imkeller and Perkowski, I introduced tools of harmonic analysis also applicable to such singular SPDEs. In collaboration with Flandoli and Priola and subsequently with some PhD students we analysed the effect of random perturbation in nonlinear infinite dimensional dynamics modelled by PDEs and we showed some situations where the presence of the noise improves the behaviour of solutions for hyperbolic and dispersive PDEs.


Project Blanc ANR ECRU “Explorations on rough paths”
Coordinator, 2009  2012
Projet Jeunes Chercheurs ANR MAGIX Mathématiques, Algèbre, Géométrie Exactes
Member, 2009 – 2012
Project B09 “Large scale modeling of nonlinear microscopic dynamics via singular SPDEs”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Principal investigator


Research Area G My main research interest is the study of partial differential equations in presence of noise.
In collaboration with P. Imkeller and N. Perkowski we developed [1] a new method to define and analyze stochastic partial differential equation with quite singular nonlinearities like the KardarParisiZhang equation, the cubic reactiondiffusion model in three dimension with additive white noise and the parabolic Anderson model in two and three dimensions, among others. In the context of the KPZ equation together with N. Perkowski we proved [2] uniqueness of energy solutions [3] for the KPZ equation. Energy solutions is a flexible tool to prove universality of fluctuations in weakly asymmetric particle systems (see e.g. [4]).
Another line of research concerns the regularizing effects of the noise in the dynamics of partial differential equations. Together with F. Flandoli and E. Priola we gave one of the first examples of regularization by noise in the context of stochastic partial differential equations [5]. In collaboration with my former Ph.D. student Khalil Chouk [6] we proved regularization by stochastic modulation in nonlinear Schrödinger equations.  Research Area C I studied path integral techniques in the analysis of certain quantum systems.
In particular, in collaboration with F. Hiroshima and J. Lörinczi [7] we explicitly constructed a measure on path space for the ground state of the renormalized Nelson Hamiltonian. This Hamiltonian describes the interaction of a Boson field with a quantum nonrelativistic particle. With J. Lörinczi [8] we constructed path integral representations for the interaction of particles with bosonic vector quantum fields, making a link with the theory of stochastic currents and rough paths.
With H. Koch and T. Oh we started the investigation of singular stochastic hyperbolic PDEs [9] which can be seen as simple models mimicking the behavior of the renormalization for quantum fields in Minkowski space or as large scale descriptions of fluctuations for nonlinear waves. 


[ 1] Massimiliano Gubinelli, Peter Imkeller, Nicolas Perkowski
Paracontrolled distributions and singular PDEs Forum Math. Pi , 3: : e6, 75 2015 DOI: 10.1017/fmp.2015.2[ 2] Massimiliano Gubinelli, Nicolas Perkowski
Energy solutions of KPZ are unique Journal of the American Mathematical Society 2017 DOI: 10.1090/jams/889[3] M. Gubinelli, M. Jara
Regularization by noise and stochastic Burgers equations Stoch. Partial Differ. Equ. Anal. Comput. , 1: (2): 325350 2013 DOI: 10.1007/s4007201300115 [ 4] Joscha Diehl, Massimiliano Gubinelli, Nicolas Perkowski
The KardarParisiZhang equation as scaling limit of weakly asymmetric interacting Brownian motions Comm. Math. Phys. , 354: (2): 549589 2017 DOI: 10.1007/s0022001729186[ 5] F. Flandoli, M. Gubinelli, E. Priola
Wellposedness of the transport equation by stochastic perturbation Invent. Math. , 180: (1): 153 2010 DOI: 10.1007/s0022200902244[ 6] K. Chouk, M. Gubinelli
Nonlinear PDEs with modulated dispersion I: Nonlinear Schrödinger equations Comm. Partial Differential Equations , 40: (11): 20472081 2015 DOI: 10.1080/03605302.2015.1073300[ 7] Massimiliano Gubinelli, Fumio Hiroshima, József Lörinczi
Ultraviolet renormalization of the Nelson Hamiltonian through functional integration J. Funct. Anal. , 267: (9): 31253153 2014 DOI: 10.1016/j.jfa.2014.08.002[ 8] Massimiliano Gubinelli, József Lörinczi
Gibbs measures on Brownian currents Comm. Pure Appl. Math. , 62: (1): 156 2009 DOI: 10.1002/cpa.20260[ 9] Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh
Renormalization of the twodimensional stochastic nonlinear wave equation arXiv preprint arXiv:1703.05461, to appear in Trans. A.M.S. 2017[10] Massimiliano Gubinelli, Nicolas Perkowski
KPZ reloaded Comm. Math. Phys. , 349: (1): 165269 2017 DOI: 10.1007/s0022001627883 [ 11] Massimiliano Gubinelli, Samy Tindel
Rough evolution equations Ann. Probab. , 38: (1): 175 2010 DOI: 10.1214/08AOP437[ 12] Massimiliano Gubinelli
Ramification of rough paths J. Differential Equations , 248: (4): 693721 2010 DOI: 10.1016/j.jde.2009.11.015[ 13] M. Gubinelli
Controlling rough paths J. Funct. Anal. , 216: (1): 86140 2004 DOI: 10.1016/j.jfa.2004.01.002



• Electronic Journal of Probability (Associate Editor, since 2011)
• Electronic Communications in Probability (Associate Editor, since 2011)
• Discrete and Continuous Dynamical Systems A (2015  2017)
• Bernoulli Journal (Area Editor, since 2015)
• Annals of Applied Probability (since 2015)
• SIAM Journal of Mathematical Analysis (since 2015)


2003  Invited professor, Institut E. Cartan, Université Nancy 1, France  2013  2018  Junior member of the Institute Universitaire de France 


2009  Minicourse on “Rough Paths”, École Polytechnique, Palaiseau, France  2012  Minicourses in Marseille, Berlin and Rome  2014  Invited lecturer at Escola Brasileira de Probabilidade, Mambucaba, Brasil and at Centro Ennio de Giorgi, Pisa, Italy  2015  Winter school “Recent Breakthroughs in Singular SPDEs”, University of MilanoBicocca, Italy  2016  CIMEEMS Summer school “Singular random dynamics”, Cetraro, Italy  2016  Minicourse at the school “Young women in probability”, Bonn  2018  Invited Section Lecture, International Congress of Mathematicians, Rio de Janeiro, Brasil 


Khalil Chouk (2013): “Trois chemins controlés”,
now Postdoc, TU Berlin
Rémi Catellier (2014): “Perturbations irrégulières et systèmes différentiels rugueux”,
now Maître de Conferences, Université Nice Sophia Antipolis, France


 PhD theses: 5, currently 3


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