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| 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, Paris-Sud 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 | Part-time Professor, École Polytechnique, Palaiseau, France | | Since 2015 | Hausdorff Chair (W3), University of Bonn |
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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 non-linear 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 non-linear 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.
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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 non-linear microscopic dynamics via singular SPDEs”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Principal investigator
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[ 1] Massimiliano Gubinelli, Nicolas Perkowski
KPZ reloaded
Comm. Math. Phys. , 349: (1): 165--269
2017
DOI: 10.1007/s00220-016-2788-3[ 2] Massimiliano Gubinelli, Peter Imkeller, Nicolas Perkowski
Paracontrolled distributions and singular PDEs
Forum Math. Pi , 3: : e6, 75
2015
DOI: 10.1017/fmp.2015.2[ 3] K. Chouk, M. Gubinelli
Nonlinear PDEs with modulated dispersion I: Nonlinear Schrödinger equations
Comm. Partial Differential Equations , 40: (11): 2047--2081
2015
DOI: 10.1080/03605302.2015.1073300[ 4] Massimiliano Gubinelli, Fumio Hiroshima, József Lőrinczi
Ultraviolet renormalization of the Nelson Hamiltonian through functional integration
J. Funct. Anal. , 267: (9): 3125--3153
2014
DOI: 10.1016/j.jfa.2014.08.002[ 5] M. Gubinelli, M. Jara
Regularization by noise and stochastic Burgers equations
Stoch. Partial Differ. Equ. Anal. Comput. , 1: (2): 325--350
2013
DOI: 10.1007/s40072-013-0011-5[ 6] Massimiliano Gubinelli, Samy Tindel
Rough evolution equations
Ann. Probab. , 38: (1): 1--75
2010
DOI: 10.1214/08-AOP437[ 7] Massimiliano Gubinelli
Ramification of rough paths
J. Differential Equations , 248: (4): 693--721
2010
DOI: 10.1016/j.jde.2009.11.015[ 8] F. Flandoli, M. Gubinelli, E. Priola
Well-posedness of the transport equation by stochastic perturbation
Invent. Math. , 180: (1): 1--53
2010
DOI: 10.1007/s00222-009-0224-4[ 9] Massimiliano Gubinelli, József Lörinczi
Gibbs measures on Brownian currents
Comm. Pure Appl. Math. , 62: (1): 1--56
2009
DOI: 10.1002/cpa.20260 |
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• 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)
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| 2003 | Invited professor, Institut E. Cartan, Université Nancy 1, France | | 2013 - 2018 | Junior member of the Institute Universitaire de France |
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| 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 Milano-Bicocca, Italy | | 2016 | CIME-EMS 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 |
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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
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- PhD theses: 5, currently 3
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