

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 


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 treelike 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, symmetrygenerated 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).


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 RO5965/11)


[ 1] Margherita Disertori, Christophe Sabot, Pierre TarrÃ¨s
Transience of edgereinforced random walk Comm. Math. Phys. , 339: (1): 121148 2015 DOI: 10.1007/s002200152392y[ 2] M. Disertori, T. Spencer
Anderson localization for a supersymmetric sigma model Comm. Math. Phys. , 300: (3): 659671 2010 DOI: 10.1007/s0022001011246[ 3] M. Disertori, T. Spencer, M. R. Zirnbauer
Quasidiffusion in a 3D supersymmetric hyperbolic sigma model Comm. Math. Phys. , 300: (2): 435486 2010 DOI: 10.1007/s0022001011175[ 4] M. Disertori, V. Rivasseau
Continuous constructive fermionic renormalization Ann. Henri PoincarÃ© , 1: (1): 157 2000 DOI: 10.1007/PL00000998[ 5] Margherita Disertori, Sasha Sodin
Semiclassical analysis of nonselfadjoint transfer matrices in statistical mechanics I Ann. Henri PoincarÃ© , 17: (2): 437458 2016 DOI: 10.1007/s000230150397x[ 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): 783825 2014 DOI: 10.1007/s0022001421021[ 7] Margherita Disertori, Alessandro Giuliani
The nematic phase of a system of long hard rods Comm. Math. Phys. , 323: (1): 143175 2013 DOI: 10.1007/s0022001317671[ 8] Margherita Disertori, Vincent Rivasseau
Random matrices and the Anderson model Random Schrödinger operators of Panor. Synth. : 161213 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): 83124 2002 DOI: 10.1007/s0022000207330[ 10] M. Disertori, V. Rivasseau
Interacting Fermi liquid in two dimensions at finite temperature. II. Renormalization Comm. Math. Phys. , 215: (2): 291341 2000 DOI: 10.1007/s002200000301




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 


 Master theses: 4, currently 2
 PhD theses: 2, currently 2


Download Profile 