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| 1996 | Diploma Thesis in Physics, University of Trento, Italy | | 1999 | PhD in Theoretical Physics, École Polytechnique, Paris, France | | 2000 - 2002 | Postdoc, Institute for Advanced Study, Princeton, NJ, USA | | 2002 - 2005 | Postdoc, ETH Zürich, Switzerland | | 2005 - 2014 | Maître de conférences, University of Rouen, France | | 2011 | Habilitation à diriger des recherches in Mathematics, Paris Diderot University (Paris 7), France | | Since 2014 | Professor (W2), University of Bonn |
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A large number of problems in modern statistical mechanics and theoretical physics can be translated into the study of suitable functional integrals. These are integrals over many variables, or more generally measures on spaces of functions or distributions.
Most of these integrals cannot be computed explicitly. Nevertheless much useful, precise information can be gained using a mixture of analytical and algebraic tools, including complex analysis and saddle point methods, multiscale analysis, rigorous renormalization group, cluster and contour expansions for functions of many variables, functional analysis on Grassman algebras, harmonic analysis on surfaces.
My current research focuses mainly on models for order/disorder transition in classical mechanics (nematic phase), quantum diffusion (random Schroedinger operators and random matrices) and stochastic processes with reinforcement (random walks in a random environment). Some of these models can be mapped into the study of certain supersymmetric nonlinear sigma models (i.e. field theories where the target space is a nonlinear manifold, described by even and odd elements in a Grassmann algebra). The symmetries of the nonlinear manifold give rise to a family of equations (Ward identities), from which much useful information can be extracted on the corresponding functional integrals.
Though a phase transition was proved for the reinforced stochastic process [1,2,3], the behavior of the system near the transition point is still out of reach (except on certain tree-like graphs). In the context of Random Schroedinger operators and random matrices, even the existence of a phase transition in dimensions larger than two remains an open problem. Supersymmetric Ward identities may help solving at least some particular examples (as the one dimensional chain). More generally, symmetry-generated identities coupled with more robust techniques such as multiscale analysis and constructive renormalization may allow to understand other open problems in stochastics, classical and quantum field theory, for example, stochastic systems without determinantal correlations (that can be represented via fermionic functional integrals) and noncommutative quantum field theories (that can be represented via interacting matrix models).
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Project A08 “Nonlinear sigma models”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”,
Principal Investigator
Oberwolfach Workshops on “The Renormalization Group”,
Organizer, 2011, 2016
“Random Schrödinger Operators arising in the study of reinforced random processes” (DFG Research Grant RO5965/1-1)
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[ 1] Margherita Disertori, Christophe Sabot, Pierre Tarrès
Transience of edge-reinforced random walk
Comm. Math. Phys. , 339: (1): 121--148
2015
DOI: 10.1007/s00220-015-2392-y[ 2] M. Disertori, T. Spencer
Anderson localization for a supersymmetric sigma model
Comm. Math. Phys. , 300: (3): 659--671
2010
DOI: 10.1007/s00220-010-1124-6[ 3] M. Disertori, T. Spencer, M. R. Zirnbauer
Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
Comm. Math. Phys. , 300: (2): 435--486
2010
DOI: 10.1007/s00220-010-1117-5[ 4] M. Disertori, V. Rivasseau
Continuous constructive fermionic renormalization
Ann. Henri Poincaré , 1: (1): 1--57
2000
DOI: 10.1007/PL00000998[ 5] Margherita Disertori, Sasha Sodin
Semi-classical analysis of non-self-adjoint transfer matrices in statistical mechanics I
Ann. Henri Poincaré , 17: (2): 437--458
2016
DOI: 10.1007/s00023-015-0397-x[ 6] Margherita Disertori, Franz Merkl, Silke W. W. Rolles
Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes
Comm. Math. Phys. , 332: (2): 783--825
2014
DOI: 10.1007/s00220-014-2102-1[ 7] Margherita Disertori, Alessandro Giuliani
The nematic phase of a system of long hard rods
Comm. Math. Phys. , 323: (1): 143--175
2013
DOI: 10.1007/s00220-013-1767-1[ 8] Margherita Disertori, Vincent Rivasseau
Random matrices and the Anderson model
Random Schrödinger operators
of Panor. Synth. : 161--213
Publisher: Soc. Math. France, Paris
2008[ 9] M. Disertori, H. Pinson, T. Spencer
Density of states for random band matrices
Comm. Math. Phys. , 232: (1): 83--124
2002
DOI: 10.1007/s00220-002-0733-0[ 10] M. Disertori, V. Rivasseau
Interacting Fermi liquid in two dimensions at finite temperature. II. Renormalization
Comm. Math. Phys. , 215: (2): 291--341
2000
DOI: 10.1007/s002200000301 |
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| 2009 | International Congress on Mathematical Physics, Prague, Czech Republic | | 2010 | Institute of Mathematical Statistics Annual Meeting, Gothenburg, Sweden | | 2010 | Invited lecture series on “Supersymmetric technique”, IMPA Rio de Janeiro, Brazil | | 2012 | SUSY and Random Matrices, IHP Paris, France |
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- Master theses: 4, currently 2
- PhD theses: 2, currently 2
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