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 will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.

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In 1913, Niels Bohr wrote his groundbreaking paper "On the Constitution of Atoms and Molecules", were he already mentioned quantum jumps between energy levels. Later on, he was also the leader of the Copenhagen interpretation of measurement. A century later, thanks to major progresses in fast electronics and low temperature physics, the delicate manipulation of simple quantum systems, and the observation of quantum jumps and quantum trajectories, have become a reality. These observations teach us important things about measurement, with deep theoretical implications, but also with practical stakes for the conception of the still elusive quantum computers. After a brief overview, we shall focus on a few recent experiments dedicated to simple quantum systems and on their theoretical interpretation which involves some remarkable probabilistic results and structures.

I shall  introduce Bohmian Mechanics and present some basic notions for the analysis of the theory. Among them the notion of typicality, which is basic  for establishing Born’s statistical law in a Bohmian universe. The talk ends with a view on relativistic quantum physics seen from a Bohmian perspective.

The physics of many-body systems strongly depends on their dimensionality. With the realization of quantum wells for example, it has been possible to produce two-dimensional gases of electrons, which exhibit properties that dramatically differ from the standard three-dimensional case, some of them still lacking a full understanding.
 
During the last decade, a novel environment has been developed for the study of low-dimensional phenomena. It consists of cold atomic gases that are confined in tailor-made electromagnetic traps. The talk will discuss some experimental aspects of this research, including dynamical features like the emergence of coherence in the gas when it is rapidly cooled across the superfluid transition.

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.

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.