# Research

I was trained in theoretical physics with a focus on statistical mechanics and nonlinear dynamics. My research interests include both fundamental questions, such as the large deviation theory approach to in and out of equilibrium statistical physics; and practical components such as the use of these tools to investigate active particles systems.

## Fluctuating hydrodynamics of active polar particles

Active particles are entities that are able to extract energy from their environment in order to ensure self-propulsion. Bacteria, animals or synthetic colloids such as Janus particles can be considered as active particles. Of particular interest are aligning active particles. Such particles can self-organise into large-scale collective motion patterns. When the number of individuals taking part into the collective motion is big, it is natural to think of this flock of active particles as a fluid. Physicists have developed hydrodynamical approaches that try to describe the large-scale motion of active aligning particles with fluid equations, such as the celebrated Toner and Tu equations. They also took into account finite number of particles effect in this equation by adding an ad-hoc noise term. We call this type of noisy equations fluctuating hydrodynamics.

During my PhD thesis, we developed a first principles based derivation of fluctuating hydrodynamics starting from microscopic toy models (such as the Vicsek model). This work is the first giving a microscopical justification of the noise term added in hydrodynamics equations that describe the large scales motions of aligning active particles.

## Large deviations and kinetic theory for long-range interacting particle systems

Statistical physics literature is very rich when it comes to describe the static fluctuations of a system around equilibrium or even its relaxation to equilibrium. For instance, working in the appropriate thermodynamic ensemble, we can express the probability of observing a given state of a system as a function of the corresponding thermodynamic potential. Beyond equilibrium, classical kinetic theories describe the relaxation to equilibrium in some asymptotic regimes. For instance the Boltzmann equation describes the relaxation to equilibrium of a dilute gas in the Boltzmann-Grad limit, and the Balescu-Guernsey-Lenard equation in the opposite limit of particles with long range interactions, for instance plasma in the weak coupling limit or self-gravitating systems. However, very few works try to describe dynamical fluctuations from the kinetic equation.

Following F. Bouchet seminal work on the dynamical large deviations from the Boltzmann equation, we obtained dynamical large deviations principles extending the Landau and the Balescu-Guernsey-Lenard kinetic theories. These large deviations principles describe the probability of any evolution path for the distribution function of long-rang interacting particles, including evolution path that are not the relaxation to equilibrium.