# Past PhD 2020

## Thibault Bonnemain

*24 fevrier 2020*

*LPTM, universite Cergy Pontoise*

*Soutenance de thèse*

*Quadratic mean field games with negative coordination*

Mean Field Games provide a powerful theoretical framework to deal with stochastic optimization problems involving a large number of coupled subsystems. They can find application in several fields, be it finance, economy, sociology, engineering … However, this theory is rather recent and still poses many challenges. Its constitutive equations, for example, are difficult to analyse and the set of behaviours they highlight are ill-understood. While the large majority of contributions to this discipline come from mathematicians, economists or engineering scientists, physicist have only marginally be involved in it. In this thesis I try and start bridging the gap between Physics and Mean Field Games through the study of a specific class of models dubbed « quadratic ».

Directeurs : Denis Ullmo, Thierry Gobron

Jury : Cecile Appert-Rolland, Olivier Gueant, Max-Olivier Hongler, Jean-Pierre Nadal, Filippo Santambrogio

## Samuel Cazayus-Claverie

*25 fevrier 2020*

*Petit amphitheatre, batiment Pascal*

*Soutenance de thèse*

*Effect of residual stress on the elasticity of fiber networks*

Cells are the basic units of all living organisms. Eukaryotic cells are stuctured on top of a scaffold of fibers ranging from stiff microtubules to semiflexible actin : the cytoskeleton. As such the cytoskeleton is involved into a broad family of processes of translocation and deformation of cells, it is also responsible for cells mechanical stiffness. The actin filaments into cytoskeleton can be cross-linked into bundles built of as much as 30 parallel filaments, but filaments can get bound at a finite angle also. These processes are in competition during network’s self-assembly and result in strong residual stresses. In this thesis, we study the effect of these residual stresses on the elasticity of fiber networks in 2 dimensions of space. We develop an original method to compute stress on the boundaries of a network and its elastic moduli. We find that residual stress induces a stiffening in the infinitesimal response of the network. Residual stress also affects the non linear response of the network : we find that it makes the network unstable under compression, and that they control the onset of non linear response to shear.

Directeur : Martin Lenz

Jury : Anael Lemaitre, Chaouqi Misbah, Giuseppe Foffi, Cecile Leduc, Raphael Voituriez

## Giampaolo Folena

*10 mars 2020*

*Universite de Rome, La Sapienza*

*Soutenance de thèse*

*The mixed p-spin models: selecting, following, and losing states*

The main driving notion behind my thesis research is to explore the connection between the dynamics and the static in a prototypical model of glass transition, i.e. the mean-field p-spin spherical model. This model was introduced more than 30 years ago with the purpose of offering a simplified model that had the same equilibrium dynamical slowing down, theoretically described a few years earlier by mode-coupling theory. Over the years, the p-spin spherical model has shown to be a very meaningful and promising model, capable of describing many equilibrium and out-of-equilibrium aspects of glasses. Eventually it came to be considered as a prototypical model of glassiness. Having such a simple but rich reference model allows a coherent examination of a subject, in our case the glass behavior, which presents a very intricate phenomenology. Thus, the main purpose is not to have a quantitative prediction of the phenomena, but rather a broader view with a strong analytical basis. In this sense the p-spin model has assumed a role for disordered systems which is comparable to that of the Ising model for understanding ferromagnetism. My research is a natural path to reinforce our knowledge and comprehension of this model.

Directeurs : Silvio Franz, Federico Ricci-Tersenghi

Jury : Luca Leuzzi, Chiara Cammarota, Patrick Charbonneau, Florent Krzakala, Luca Dall'Asta, Pierfrancesco Urbani,