Here you can find some of my lecture notes, based on different courses I have given, mostly at the University of Geneva. The notes are in English, unless stated otherwise.
Les Diablerets lectures on resurgence in mathematics and physics
This is the text of lectures given in Les Diablerets school on Mathematical Physics, in January 2021. They provide a gentle introduction to the theory of resurgence and to its applications in physics and mathematics. You can download them here.
Path integrals in quantum theory
This is a course at the doctorate level on path integrals in quantum theory. It starts with the standard path integral formulation of the quantum mechanics of a single particle, and moves on to derive the path integral formulation of quantum many-particle systems. The general formalism is illustrated with applications to interacting quantum gases. The lecture notes can be found here.
This is an advanced undergraduate level course on statistical mechanics. An interesting peculiarity of the course is that it contains an introduction to two of the most beautiful models in non-equilibrium statistical physics: the Kac ring model, and the Ehrenfest urn model. You can download the lecture notes (in French) here.
An introduction to topological quantum field theory
This is an introduction to topological quantum field theory at the master level. Shortly after the beginning of the course, COVID and confinement took over our lives and I never got as far as I was planning. The course contains however an introduction to supersymmetry and to the Mathai-Quillen formalism, and a discussion of the Witten index in supersymmetric quantum mechanics. You can download the lecture notes here.
Mathematical models for animals and humans
This course is an introduction to mathematical modelling based on game theory. It contains applications to economics and to animal behaviour. Although I never did research in this field, game theory has been a hobby of mine for some time now, and I was lucky enough to transform this hobby into a fun course. You can download the lecture notes here.
Classical and quantum mechanics for mathematicians
Here is the challenge: you have thirty-two hours to teach both classical and quantum mechanics to mathematicians, at the master level. What do you do? This was, alas, no thought experiment, but a real one. The lecture notes resulting from the experiment can be found here. I hope they are useful.
An introduction to differentiable manifolds
This is an introduction to differentiable manifolds for advanced undergraduates in mathematics. The lecture notes (in French) can be downloaded here.
Quantum field theory in curved space
This is a course on quantum field theory in curved space at the master/doctorate level. I confess that I gave this course to learn the subject and in the process I discovered that I don't like it that much. Therefore, it is not a very insightful course, although it is very detailed and can still be useful. You can find the lecture notes here.
An introduction to non-perturbative effects in string theory and AdS/CFT
In 2015 I gave a series of lectures at ICTP in Trieste on non-perturbative effects in AdS/CFT and in string theory, where I start with a general introduction from the point of view of resurgence. The lecture notes can be found here.
Topological field theory and four-manifolds
These are the notes of a course I gave long ago in Villa de Leyva (Colombia). It is probably superseded by my joint book with José Labastida, but it might be still useful for learning the subject. You can find the lecture notes here.
This is an undergraduate course on hyperbolic geometry and general topology. The lecture notes (in French) can be found here.