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MARC MEZARD

MARC MEZARD
Full Professor
Department of Computing Sciences

Courses a.y. 2022/2023

30558 STATISTICAL AND QUANTUM PHYSICS
41002 STATISTICAL MECHANICS AND METHODS FOR COMPLEX SYSTEMS

Biographical note

I am a Professor of Theoretical Physics. I studied physics at Ecole normale supérieure in Paris and I obtained my PhD in 1984. Hired at CNRS in Paris, I was Research Director in Université Paris Sud. From 2012 and 2022 I became Director of Ecole normale supérieure, and I then joined Bocconi University as a professor, in the newly created department of computational sciences.  My work focuses on statistical physics of disordered systems, with applications in various fields like information theory, computer science, machine learning, biophysics.


Research interests

I am interested in the emergent phenomena in complex systems with many interacting “atoms”, (that could be for instance agents on a market, information bits, or molecules are different or live in different environments. The statistical physics of disordered systems that I contribute to develop finds applications in various branches of science – biology, economics and finance, information theory, computer science, statistics, signal processing. In recent years my research has focused on information processing in neural networks, machine learning and deep networks. I am particularly interested in the theoretical impact of data structure on learning strategies and generalization performance.


Selected Publications

Mézard, Parisi, Sourlas, Toulouse, Virasoro
On the nature of the spin glass phase
Phys. Rev. Lett. 52, 1984

M. Mézard and G. Parisi
Replicas and optimization
J. Physique Lett. 46, 1985

M. Mézard, G. Parisi and M.A. Virasoro
SK model: the replica solution without replicas
Europhys. Lett. 1 (1985) 77, 1985


W. Krauth and M. M'ezard
Storage capacity of memory networks with binary couplings
Journal de Physique 50 (1989) 3057., 1989

C. Bouchiat and M. Mézard
Elasticity model of a supercoiled DNA molecule
Phys. Rev. Lett. 80 (1998) 1556, 1998

M. Mézard and G. Parisi
Thermodynamics of glasses: a first principle computation
J. Phys. Condens. Matter 11 (1999) A157-A165., 1999

M. Mézard and G. Parisi
The Bethe lattice spin glass revisited
Eur. Phys. J. B 20 (2001) 217, 2001

M. Mézard, G. Parisi, R. Zecchina
Analytic and Algorithmic Solution of Random Satisfiability Problems
Science 297 (2002) 812, 2002

Marc Mézard, Andrea Montanari
Reconstruction on trees and spin glass transition
, J. Stat. Phys. 124 (2006) 1317-1350, 2006

Stephan Mertens, Marc Mezard, Riccardo Zecchina
Threshold values of Random K-SAT from the cavity method
Arxiv, 2006

Florent Krzakala, Marc Mézard, Francois Sausset, Yifan Sun and Lenka Zdeborova
Statistical physics-based reconstruction in compressed sensing
Phys. Rev. X 2 (2012) 021005, 2012

Emmanuelle Gouillart, Florent
Belief Propagation Reconstruction for Discrete Tomography
Inverse Problems 29, 3 (2013) 035003, 2013

Sebastian Goldt, Marc Mézard, Florent Krzakala and Lenka Zdeborova
Modelling the influence of data structure on learning in neural networks: the hidden manifold model
Phys.Rev. X.10.041044, 2019

Federica Gerace, Bruno Loureiro, Marc Mézard, Florent Krzakala and Lenka Zdeborova
Generalization in learning with random features and the hidden manifold model
International Conference of Machine Learning, ICML 2020, 2020

Antoine Baker, Indaco Biazzo, Alfredo Braunstein, Giovanni Catania, Luca Dall'Asta, Alessandro Ingrosso, Florent Krzakala, Fabio Mazza, Marc Mézard, Anna Paola Muntoni, Maria Refinetti, Stefano Sarao Mannelli, Lenka Zdeborova
Epidemic mitigation by statistical inference from contact tracing data
, PNAS (2021 ): 118 (32) e2106548118, 2021