The first year of the Master’s degree includes mandatory lectures such as Statistical Physics, Quantum mechanics, Experimental Physics, etc, and specialised classes. Students of the “Complex Systems & Living Systems” program are invited to choose the following lectures among the options offered by the Master’s degree:

• Dynamical Systems (4 ECTS): This course explores how dynamical systems evolve over time based on their parameters. It focuses on identifying stable states, cyclic patterns, and the effects of parameter changes on the system's behaviour. The systems are modelled using ordinary differential equations, and key concepts such as attractors, stability/instability, and bifurcation points are covered.
• Continuous Media (4 ECTS): This course covers the dynamics of deformable continuous media, focusing on fluids. It explores fluid flow characteristics, transport phenomena, and the governing equations such as Navier-Stokes and Fourier laws. Topics also include non-dimensional numbers, viscous regimes, and vorticity dynamics.
• Physics of Living Systems (4 ECTS): This course examines the physics principles that govern the organization and dynamics of living systems. It explores how living organisms, despite their complexity, can be understood using concepts and technologies from different areas of physics.
• Internship (4 ECTS): students will have the possibility to do a 7-week internship in one of the lab of the CENTURI community.

The second year of the Master’s degree consists in core courses and specialised courses which can be freely chosen by the students. For the “Complex Systems & Living Systems” track we recommend the following courses:

• Complex Matter (6 ECTS): This course will introduce a theoretical description of complex matter to model biological systems such as active tissues as well as flock of birds. In parallel, students will work on research projects in different labs of the CENTURI community.
• Statistical Physics II (6 ECTS): This course covers the theoretical aspects of stochastic systems, from random walks to Markov chains, and analytical tools from Fokker-Planck equations to the Fluctuation-dissipation theorem. It will further present fundamentals on Percolation theory, Boltzmann equations and ties between Information theory and Statistical Physics, both analytically and numerically.
• Dynamical Systems & Non-linear Physics (6 ECTS): This course covers core and advanced concepts of dynamical systems and chaos, including non-linear systems, differential equations, and vector fields. It explores local properties such as stability, attractors, and bifurcations. Global properties discussed include Cantor sets, invariant measures, and entropy. The course also delves into Hamiltonian systems, chaos theory, instabilities, self-organization, and the emergence of patterns. Additionally, it examines the road to chaos in dissipative systems through bifurcations, sensitivity to initial conditions, and intermittent behaviour.
• Advanced Quantum & Statistical Field Theory (4 ECTS): This interdisciplinary course provides theoretical tools from Field theory common to both quantum and statistical physics. It explores length scales in physics, covering critical phenomena, Landau-Ginzburg theory, Wilson's renormalisation group approach, path integrals and Feynman rules, fixed points, asymptotic behaviour, and effective field theories. It is especially designed to be accessible to students from various fields with interest in the concept of renormalisation.
• Soft Matter (4 ECTS): Soft Matter refers to materials where interactions between particles (molecules, macromolecules, etc.) are weak, allowing for easy deformation by external forces. Soft materials exhibit diverse structures, unique symmetry groups, and phases dominated by defects. The prevalence of entropy-driven states and transitions, along with the relevance to everyday materials, active matter, and living systems, makes Soft Matter a fascinating field of study.
• Complex Networks (4 ECTS): This course covers the representation of complex networks and the use of network representations, along with statistical characterization of networks, including paths, degrees, centrality, community detection, and degree distribution. It explores network models such as random graphs, preferential attachment, and the copy model. It uses examples from social phenomena, epidemiology and neurology.
• CENTURI Hackathon (4 ECTS): Students will have the opportunity to participate to the Hackathon organized by CENTURI. Participants will work on big data projects for living systems, with projects from academic labs in CENTURI and elsewhere. The aim is to solve key technological bottlenecks in a variety of topics, such as Computer vision, Modelling, Data mining and Computer assisted microscopy.
• Internship: A 4-month internship is a mandatory part of the Master’s degree. Students from the CSLS program will have the opportunity to do it in one of the lab of the CENTURI community.