MicroRNAs are recently discovered regulators of gene expression, coordinating many biological processes. They are especially important for developmental processes, including cell differentiation, while their deregulation causes diseases like cancer.
In particular, microRNAs are key regulators of muscle differentiation, a complex process necessary for the formation of muscle fibers. I’ll describe the regulation of skeletal muscle differentiation by the miR-98 – E2F5 molecular pathway.

The linear Schrödinger equation does not predict the uniqueness of  measurement results;  it does not predict that macroscopic bodies should  be located at one place in space only. This is the origin of the so  called measurement problem, Schrödinger cat paradox, etc. Theories such  as GRW (Ghirardi-Rimini-Weber) and CSL (Continuous spontaneous  localization) theories solve the problem by adding stochastic terms to  the Schrödinger equation. In this talk we will propose another approach  to reach the same unified dynamics, but without requiring the  introduction of stochastic Wiener processes acting in all space. The  method combines ideas of the dBB (de Broglie Bohm) interpretation and of  CSL. It introduces an attraction between the space density of Bohmian  position and the space density operators, with a deterministic dynamics;  randomness arises only from the initial random positions of the Bohmian  positions. Various microscopic or macroscopic consequences of this  dynamics will be discussed.

L'effet Hall fractionnaire est un des phénomènes les plus surprenants de la physique de la matière condensée. Il se manifeste via les propriétés de transport de gaz d'électrons bi-dimensionnels soumis à des champs magnétiques intenses. Cette physique pourrait également être reproduite dans des expériences avec des atomes froids, par exemple dans un gaz de bosons en rotation rapide.

La fonction d'onde de Laughlin, proposée comme une approximation pour le fondamental de tels systèmes, est à la base de notre compréhension actuelle de ce phénomène, mais certaines de ses propriétés fondamentales sont encore mal comprises d'un point de vue mathématique. Cette fonction d'onde décrit un fluide quantique hautement corrélé et il est en particulier crucial d'élucider l'aspect robuste de ses corrélations.

Dans cet exposé on étudiera un modèle pour la réponse de la fonction de Laughlin aux variations d'un potentiel extérieur. Cela nous conduira à une famille de problèmes variationnels d'un type nouveau. Nos résultats principaux sont des estimations d'énergie rigoureuses indiquant une forte rigidité dans la réponse de l'état  de Laughlin à la variation du potentiel extérieur.

Travail commun avec Jakob Yngvason.

Quantum theory is remarkably consistent and beautiful. Yet, as a theory on an experimental science, it ought to tell us what is measurable and how to extract information about Nature from these measurements. It also ought to tell us how Nature produces correlations between disconnected regions that can’t be described using only local variables that propagated gradually and continuously through space. Staring at these two problems might not help to find the next theory. But it provides much inspiration to design experiments that illuminate the situation and might, some day, help in finding the limits of quantum theory. I’ll discuss these two problems and their different status. Next, I'll present several such experiments.

Mixed twistor D-modules are D-modules with mixed twistor structure. The notion of twistor structure is a generalization of that of Hodge structure, introduced by C. Simpson. As in the Hodge case, various operations for D-modules are enhanced to those for mixed twistor D-modules. It implies that some important mathematical objects are naturally equipped with mixed twistor structure. For example, the D-modules associated to families of Laurent polynomials, called the GKZ hypergeometric systems, are naturally equipped with mixed twistor structure. It looks natural to pursuit their roles in the Hodge theoretic aspect of mirror symmetry. In this talk, I am planning to discuss the degeneration of twistor structure associated to the degeneration of Landau-Ginzburg models, and to explain how the isomorphism of Givental induces an isomorphism of mixed TEP-structures in the local mirror symmetry for Fano toric manifolds.

According to quantum theory, the outcomes of measurements are  generally not deterministic. "Single-world" theories (such as Bohmian  mechanics) add additional elements to quantum theory in order to restore determinism. In this talk, I will argue that such single-world theories  cannot be self-consistent in the following sense: any attempt to use a single-world theory to describe an observer who himself applies the  theory necessarily results in a contradiction.

The two concepts in the title stand for two distinct quantum phenomena whose relation to one another is not obvious although they often occur together.  Moreover, there is not a unique concept of superfluidity. In the talk I shall first comment on these general issues and then discuss a simple model involving a tunable random potential where some precise statements can be rigorously proved. The latter is joint work with M.Könenberg, T. Moser and R. Seiringer.

I shall give a quick introduction to the model of repeated quantum interactions and their continuous-time limit. I shall also connect them to quantum trajectories. This approach to open quantum systems makes quantum noises appearing very naturally and it shall be the occasion to present these tools, which are not so commonly shared by the physicist community.