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Prof. Dr. Massimiliano Gubinelli former Hausdorff Chair |
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| Academic Career | |||||||||||||||||
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| Awards | |||||||||||||||||
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| Invited Lectures | |||||||||||||||||
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| Editorships | |||||||||||||||||
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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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| Research Projects and Activities | |||||||||||||||||
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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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| Research Profile | |||||||||||||||||
| 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. | |||||||||||||||||
| Selected PhD students | |||||||||||||||||
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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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| Selected Publications | |||||||||||||||||
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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 [10] M. Gubinelli
Controlling rough paths J. Funct. Anal. , 216: (1): 86--140 2004 DOI: 10.1016/j.jfa.2004.01.002 |
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| Publication List | |||||||||||||||||
