Disordered systems out of equilibrium
Leticia F. Cugliandolo
Université Paris Sorbonne
France
- Introduction. Quenched and configurational disorder. Coarsening. Glassiness and active matter. Models and methods.
- Equilibrium analysis. Free-energy landscapes (extensions of Ginzburg-Landau).
- Out of equilibrium dynamics. Dynamic mean-field theory.
Threeway out of equilibrium many body dynamics
Frédéric van Wijland
Université Paris Cité
France
These three lectures will focus on three manners to fall out of equilibrium, and on the many-body effects that arise from the nonequilibrium nature of the dynamics. We will begin with systems harboring a macroscopic current (leading to long range correlations). Then we shall stop by systems that should be relaxing towards equilibrium, but that fail to do so for reasons that are still under investigation. And the final lecture will concern systems with no macroscopic current that are nevertheless maintained out of equilibrium by a constant input of energy that drives the individual motion of the particles.
- Out of equilibrium with a macroscopic current: Driven Systems
- Macroscopic Fluctuation Theory
- The possibility of phase transitions in one dimension
- Out of equilibrium, but lost on the way to equilibrium: Glasses
- Mode-coupling approach
- Infinite-dimensional insight
- Out of equilibrium, because that's life: Active Matter
- From one particle to many
- Field theories for active matter
A statistical physics perspective on the theory of machine learning
Bruno Loureiro
École Normale Supérieure, Paris
France
The past decade has witnessed a surge in the development and adoption of machine learning algorithms to solve day-a-day computational tasks. Yet, a solid theoretical understanding of even the most basic tools used in practice is still lacking, as traditional statistical learning methods are unfit to deal with the modern regime in which the number of model parameters are of the same order as the quantity of data – a problem known as the curse of dimensionality. Curiously, this is precisely the regime studied by Physicists since the mid 19th century in the context of interacting many-particle systems. This connection, which was first established in the seminal work of Elisabeth Gardner and Bernard Derrida in the 80s, is the basis of a long and fruitful marriage between these two fields.
The goal of this mini-course is to provide an in-depth overview of these connections and a good vision of the different tools available in the statistical physics toolbox, as well as their scope and limitations.
Syllabus:
- Historical overview of the connections between Statistical Physics and Computer Science.
- Mean-Field Models 101: Curie-Weiss Model
- Statistical-to-Computational Gaps
- The double-descent phenomena and benign overfitting (time permitting)
Bibliography:
The mini-course will the based on the following lectures notes: https://brloureiro.github.io/assets/pdf/NotesPrinceton_BL.pdf
