Many motile photosynthetic micro-organisms have the ability to orient themselves in light fields, a property called “phototaxis”. This phenomenon, usually mediated by a specialised organelle called the eyespot (composed of photo-sensitive molecules), is still poorly understood. Modelling such process is difficult because we lack information on how the temporal light signal received at the eyespot as the cell rotates along its swimming axis is interpreted and converted to a modulation of the flagellar beating (to impose a torque on the cell body and reorient in the correct direction). Here we propose to investigate this still open question in the model micro-alga Chlamydomonas reinhardtii by quantifying single-cell trajectories in well-controlled illumination landscapes while imaging the location of the eyespot. This will allow correlating the cell motion with the inferred temporal signal received at the eyespot along the trajectory. In addition we will investigate phototaxis at the population level, where light-matter interaction (absorption) with the cell population feedbacks on the phototactic behavior of the cells and can lead to emergent phenomena, such as collective modes of phototaxis. By bringing further knowledge on single-cell and collective phototaxis we will aim to finely control the individual and collective phototactic transport of the cells under dynamic light patterns. This will constitute a proof of concept that light can be exploited in concrete applications, such as micro-algal biomass harvesting in industrial bioreactors, step that is the current energetic and financial bottleneck in the micro-algal industry (which aims to produce low-carbon footprint biofuels, food, drugs, etc). In addition, building on existing models of phototaxis will help to better describe phytoplanktonic population dynamics in natural environments where phototaxis plays a crucial role.

Complex random systems with many degrees of freedom, or constituted of many interacting particles, often display a universal behaviour at large scale. This means that scaling exponents, and even the precise statistics of random fluctuations of macroscopic quantities, are largely independent of the specifics of the model and the details of the interaction rules. Hence, within one universality class, a lot of information can be obtained from the study of one integrable, i.e. exactly solvable, toy-model in the class. The field of integrable probability is the art of designing and studying such models, using a wide range of tools from stochastic analysis, algebraic combinatorics, random matrix theory, representation theory and quantum integrable systems. In particular, it fueled important progress in recent years about the Kardar-Parisi-Zhang (KPZ) universality class, a class of models describing random interface growth and fluctuations of random paths in random media. This project aims at developing new frameworks to deal with models in the KPZ class, that are important to compare theoretical predictions with experimental settings. Applications will include the study of fluctuations in systems of interacting particles with boundaries and the estimation of hitting times of extreme diffusions in random media. Another objective is to bring the tools of integrable probability outside the KPZ class, to study random surfaces associated to non-intersecting diffusions in random media and non-commutative analogues of models in the KPZ class. Along the way, we will generalize several of the beautiful mathematical structures that underlie stochastic integrability.

Life-threatening cues such as a sting in the foot cause immediate avoidance behavior. In that moment, the prompt integration of sensory inputs by motor centers can become a matter of life and death. A major challenge in neuroscience is to understand how information flows in the brainstem during such integrative reflexive behaviors by assessing the direction of neuronal communication or causality. Although correlation analysis of neural activity signals is widely used to estimate functional connectivity, this method lacks causality information underlying the direction of information flow. LOCONNECT will build a framework for understanding how sensorimotor integration is achieved by combining optical recordings of intracellular calcium dynamics from spatially distributed command neurons in the brainstem (Wyart group at the Paris Brain Institute) with a theoretical framework that identifies causality (Mora group at the Ecole Normale Supérieure).

Conformal Field Theories (CFTs) have a wide range of experimental and theoretical applications: describing classical and quantum critical phenomena, where they determine critical exponents; as low (or high) energy limits of ordinary quantum field theories; and as theories of quantum gravity in disguise via the AdS/CFT correspondence. Unfortunately, most interesting CFTs are strongly interacting and difficult to analyse. On the one hand, perturbative and renormalization group methods usually involve approximations that are hard to control and which require difficult resummations. On the other hand, numerical simulations of the underlying systems are difficult near the critical point and can access only a limited set of observables. The conformal bootstrap program is a new approach. It exploits basic consistency conditions which are encoded into a formidable set of bootstrap equations, to map out and determine the space of CFTs. A longstanding conjecture states that these equations actually provide a fully non-perturbative definition of CFTs. In this project we will develop a groundbreaking set of tools – analytic extremal functionals – to extract information from the bootstrap equations. This Functional Bootstrap has the potential to greatly deepen our understanding of CFTs as well as to determine incredibly precise bounds on the space of theories. Our main goals are A) to fully develop the functional bootstrap for the simpler and mostly unexplored one-dimensional setting, relevant for critical systems such as spin models with long-range interactions and line defects in conformal gauge theories, leading to analytic insights and effective numerical solutions of these systems; and B) to establish functionals as the default technique for higher dimensional applications by developing the formalism, obtaining general analytic bounds and integrating into existing numerical workflows to obtain highly accurate determinations of critical exponents.

The goal of this project is to implement an autonomously protected quantum bit (qubit) in a high impedance Josephson circuit parametrically modulated by a magnetic field with a frequency comb structure. In an extreme impedance regime now attainable in circuitQED experiments, coherent charge tunneling across a resonant circuit induces an infinite order non-linearity on the circuit photons. Our protocol exploits optimally this effect in order to synthesize, in a reduced model, a fully non-local dynamics whose two lowest-energy stationary states coincide with the Gottesman-Kitaev-Preskill bosonic code. This logical qubit is stabilized in a straightforward way by reservoir engineering, and is topologically protected against most decoherence channels plaguing superconducting circuits. For realistic experimental parameters, the residual logical error rate is expected to be orders of magnitude lower than the underlying circuit dissipation rate.