Master 2 courses in Physics - Physics Complex Systems track
The International Master Physics of Complex Systems is a research-oriented French-Italian programme in fundamental physics. It focuses on statistical physics, equilibrium and non-equilibrium phenomena, dynamical systems, stochastic processes, nonlinear physics, numerical simulation, and interdisciplinary applications to complex systems. It is intended for students interested in the formal aspects of physics.
The programme is taught in English and has a strong international dimension, with partner institutions in Paris, Torino and Trieste. For this document, Teaching Group 1 corresponds to September-December and Teaching Group 2 to January-March.
Teaching group 1 [September-December]
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Introduction to nonlinear physics through hydrodynamics, elasticity, and soft matter. The course covers linear and weakly nonlinear problems, bifurcations, asymptotic methods, singularities, self-similar solutions, dynamical systems, chaos, and turbulence.
Prerequisites: General background in physics, differential equations, and applied mathematics.
Contact: Bruno Andreotti (Université Paris Cité)
Master year: M2 - Semester 1 - 6 ECTS
Brief description: Course on the modelling and understanding of stochastic phenomena. It covers probability with emphasis on large deviations, Markov processes, Langevin and Fokker-Planck equations, stochastic calculus, fluctuation theorems, first-passage properties, Brownian-motion functionals, and the Feynman-Kac formula.
Prerequisites: General background in probability, statistical physics, and applied mathematics.
Contact: Christophe Texier (Université Paris-Saclay)
Master year: M2 - Semester 1 - 6 ECTS
Brief description: Introduction to core concepts and algorithms of machine learning for physicists. The course covers supervised and unsupervised learning and is accompanied by Python notebooks to test the main algorithms and introduce widely used ML packages.
Prerequisites: General background in physics, statistics, and basic scientific programming.
Contact: Martin Weigt (Sorbonne Université)
2nd year Master - 1st Semester - 6 ECTS - English Level: B2 (no test required)
Brief Description
Machine learning (ML) is one of the most dynamic and exciting areas in modern datadriven research. Built upon inspiration from fields as different as statistics, computer science, neurosciences and physics, it allows for automatic learning from complex large-scale datasets. The lectures aim at introducing the core concepts and algorithms of ML in a way easily understood by physicists, both in the setting of supervised learning (linear and logistic regression, ensemble methods, deep neural networks…) and unsupervised learning (dimensional reduction, clustering, generative modelling…). The course is accompanied by Python Jupiter Notebooks, which allow for testing the main algorithms presented in the lectures, and introduces some highly used ML Python packages to the students.
Contact
Dominique Mouhanna (dominique.mouhanna@sorbonne-universite.fr)
Master year: M2 - Semester 1 - 6 ECTS
Brief description: Course on statistical field theory for systems with large-scale fluctuations. It introduces coarse-graining, effective Hamiltonians, functional integrals, Feynman diagrams, critical phenomena, and renormalization-group methods.
Prerequisites: Statistical physics and mathematical methods for physics.
Contact: Dominique Mouhanna (Sorbonne Université)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Elective course centered on morphogenesis and the mechanistic origin of forms. It connects nonlinear physics with questions ranging from planet formation, landscapes, clouds, and cyclones to animal motion, microorganisms, embryos, populations, and global warming.
Prerequisites: General background in nonlinear physics and continuum modelling is recommended.
Contact: Bruno Andreotti (Université Paris Cité)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Introduction to classical disordered systems and to the theoretical concepts used to study their equilibrium and out-of-equilibrium physics. Topics include metastability, rough energy landscapes, slow dynamics, avalanches, glasses, optimization, inference, and learning problems.
Prerequisites: Statistical physics and probability are recommended.
Contact: Valentina Ros (LPTMS, Université Paris-Saclay)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Course on tools developed to study non-equilibrium systems. The first part treats relaxation toward thermal equilibrium through Langevin equations, Ito calculus, Fokker-Planck equations, and master equations; the second part applies these tools to active matter.
Prerequisites: Statistical physics, stochastic processes, and basic differential equations are recommended.
Contact: Frédéric van Wijland (Université Paris Cité)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Elective course showing how statistical field theory applies both to critical phenomena and to soft-matter systems such as polymers, membranes, interfaces, and liquid crystals, where strong thermal fluctuations play a central role.
Prerequisites: Statistical physics and field-theory basics are recommended.
Contact: Jean-Baptiste Fournier (Université Paris Cité)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Introduction to how physics can inform the study of living systems, from sub-cellular to organism scales. The course links development, symmetry breaking, collective motion, cytoskeleton, membranes, and tissue mechanics with ideas from nonlinear physics, soft matter, and non-equilibrium statistical physics.
Prerequisites: General physics background; soft matter and statistical physics are helpful.
Contact: Andrew Callan-Jones (Université Paris Cité)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Lectures introducing theoretical methods for the out-of-equilibrium dynamics of quantum complex systems. Topics include quantum baths, quenched randomness, quantum chaos, and quench dynamics, with parallels to classical counterparts.
Prerequisites: Quantum mechanics and statistical physics are recommended.
Contact: Leticia Cugliandolo (Sorbonne Université)
Master year: M2 - Semester 1 - 3 ECTS
Brief description: Course introducing basic theoretical tools for quantum information and computation. After a review of quantum mechanics, it presents the quantum circuit model, simple quantum algorithms, quantum error correction, and, time permitting, questions related to quantum computational supremacy.
Prerequisites: Quantum mechanics and linear algebra are recommended.
Contact: Arne Keller (Université Paris-Saclay)
Teaching group 2 [January-March]
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Course on classical nonequilibrium systems that are flowing, growing, or evolving. It presents different types of nonequilibrium dynamics and tools used to study irreversibility, collective behaviour, coarsening, exclusion processes, interface growth, flocking, and active matter.
Prerequisites: Statistical physics and differential equations are recommended.
Contact: Alexandre Solon (CNRS-Sorbonne Université)
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Course on random-matrix methods for complex and disordered systems. It emphasizes the use of random matrices to study spectral properties and to tackle problems arising in statistical physics, condensed matter, quantum chaos, evolutionary game theory, and finance.
Prerequisites: Linear algebra, probability, and statistical physics are recommended.
Contact: Ada Altieri (Université Paris Cité)
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Follow-up to Computational Science combining lectures and lab sessions. Students code algorithms from scratch and apply them to textbook and real-life datasets while learning the mathematical foundations, methodological issues, and statistical-physics interpretation of modern machine-learning methods.
Prerequisites: Computational Science or equivalent background in machine learning and Python is recommended.
Contact: Volker Bormuth (Sorbonne Université)
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Course showing how tools from the statistical physics of nonequilibrium and disordered systems can be used to study ecosystems. Topics include ecological patterns, fluctuating population dynamics, extinction, spatial structure, interacting populations, stability, chaos, and dynamical mean-field theory.
Prerequisites: Statistical physics and differential equations are recommended.
Contact: Thibaut Arnoulx de Pirey (CEA)
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Set of lectures presenting a statistical-physics approach to financial markets. It covers Brownian-motion modelling, price formation from many interacting agents, option pricing, risk, portfolio optimization, and covariance-matrix analysis with links to random matrix theory.
Prerequisites: Probability, stochastic processes, and statistical physics are recommended.
Contact: Marco Tarzia (Sorbonne Université)
Master year: M2 - Semester 2 - 3 ECTS
Brief description: Course on transport models across systems as different as cities and the cell interior. It studies microscopic, mesoscopic, and macroscopic descriptions inspired by fluid models, conservation laws, and competition for space, including game-theory aspects.
Prerequisites: Continuum mechanics, differential equations, and modelling basics are recommended.
Contact: Cécile Appert-Rolland (Université Paris-Saclay)
Master year: M2 - Semester 2 - 18 ECTS
Brief description: 3 month internship
Contact: Maxim Dolgushev (Sorbonne Université)
Master year: M2 - Semester 2 - 12 ECTS
Brief description: one month of courses in Trieste
Contact: heads of the master