I will review supersymmetric localization techniques, focusing on two-dimensional gauge theories. I will then apply them to the computation of the supersymmetric partition function on the sphere and the torus, producing matrix models. I will finally make connections with vortex partition functions, Gromov-Witten invariants, cluster algebras and the elliptic genus.

The CNRS/Solvay Joint Laboratory (UMR: Unité Mixte de Recherche) 'Advanced Polymer Materials Laboratory' (LPMA), located near Lyon, France, has been created in September 2006. Thanks to the fundamental research work developed in the lab, Solvay intends to propose innovative materials with tailored properties to answer to three main challenges: lightweight solutions for transportation, enhanced barrier properties for environmental safety and mastering of the life cycle of engineering plastics and rubbers. To achieve these challenging goals, the lab gathers CNRS researchers, who pursue academic careers, and Solvay researchers, shaping potential industrial applications. In this talk I will explain briefly how the lab works and how our strategy tackles topics relevant to applications and industrial issues by developing entirely new ideas relevant to fundamental concepts of polymer physics. I will exemplify this strategy by focusing on our recent developments on molecular modeling on silica filled rubbers and on our experimental work on the understanding of polymer blends.

I consider the concept of geometrical CP violation focusing on Delta(27) models. I discuss the scalar potential responsible for the spontaneous CP violation with calculable phases and give details on the issues that arise when introducing fermions compatible with geometrical CP violation. The minimal model with viable quark masses will be introduced as well as structures that lead to the observed lepton masses and mixing, which combined provide an existence proof of geometrical CP violation models accounting for the masses and mixing of all fermions.

The problem of the solid fracture has occupied scientists and engineers for centuries. This phenomenon is classically addressed within the framework of continuum mechanics. Still, stress enhancement at crack tips makes the failure behavior observed at the continuum-level scale extremely dependent on the presence of microstructure inhomogeneities down to very small scales. This yields statistical aspects which, by essence, cannot be addressed using the conventional engineering continuum approaches. I addressed this problem from two different points. First, I designed an experimental setup that allows growing well-controlled tensile cracks in brittle heterogeneous solids of tunable microstructure, over a wide range of loading speed. The crack dynamics and the evolution of stored and released mechanical energy are monitored in real time. In parallel, the acoustic emission going along with crack growth is recorded via a series of acoustic transducers, and analyzed in a way similar to that develop by geophysicists to process seismic signals. The experiments allowed me to characterize quantitatively the crackling dynamics of cracks, also to evidence intriguing statistical similarities between the seismicity associated with this simple situation of a single running crack under tension and the much more complex situation of multicracking in compressive fracture and in earthquakes. In parallel, I addressed the problem numerically. The simulations invoke a recent statistical model mapping heterogeneous fracture with the depinning transition of an elastic manifold in a random potential. The numerical exploration of the parameter space allowed me to unravel when (i.e. which loading conditions, microstructure material parameters, material constants...) regular dynamics compatible with continuum approaches are expected to be observed, and when crackling dynamics calling for statistical approaches are observed. In this latter case, we have characterized quantitatively the dynamics statistic and its variations as a function of the input parameters.

We will discuss about the coupling between the classical thermal environment and a mesoscopic system. Around this theme, we will deal with several questions : Is the heat bath always in equilibrium? How can we compare the fluctuation-dissipation relations of the 1st kind and the 2nd kind? How the energy is exchanged between the heat bath and the system? Does this energy, or heat, depend on the scale of description? What aspects are the Langevin equation unable to describe? How can we see the spatio-temporal non-locality of the heat bath? Are the `Casimir' type reversible forces related to the frictional memory forces ?

Les azopolymères sont une classe de matériaux photo-actifs qui peuvent être utilisés pour former des structures ordonnées. Ces polymères sont sensibles à la variation du champ électrique de la lumière qui crée une force au niveau de la couche. En utilisant un interféromètre de type Mach-Zehnder, il est possible de produire des réseaux d’interférence sur l’échantillon qui forme la base de la structure à fabriquer. Typiquement, ces structures ont la forme de réseaux unidimensionnels où la hauteur dépend du temps d'exposition et de la fluence de la lumière incidente. Nous avons récemment utilisé cette méthode pour fabriquer des couches minces ferromagnétiques structurées avec une anisotropie magnétique induite contrôlée par la structure. La méthode pompe - sonde est une technique optique basée sur l'utilisation de lasers ultra-rapides et permet des mesures physiques résolues en temps. Dans la deuxième partie du séminaire, je présenterai la mise en place d’un spectromètre pompe - sonde ainsi que des mesures de la dynamique magnétique avec une résolution temporelle de moins de 8 fs. Je décrirai ensuite le montage expérimental et donnerai quelques exemples de réalisations récentes.

The Institut Laue-Langevin (Grenoble, France) provides neutrons for the whole scientific community. In order to transport those particles tens of meters from the reactor, neutron guides have been implanted around the core. In most cases, they consist in 4 glass plates, coated with Nickel or Nickel-Titanium, assembled in a rectangular shape. As the reflectivity of the mirror is below 100%, the glass faces irradiation and may end up cracking. The microscopic mechanisms of this phenomenon will be exposed, as well as the future experiments that will be conducted to explain the behaviour dissimilarities among the different glasses used at ILL.

The temporal behavior of polarized reflection spectra of a microcavity with a 20-nm quantum well is experimentally studied by means of polarized pump-probe technique. Kerr rotation and ellipticity are obtained for different detunings between exciton and photon modes. The Kerr rotation signal was determined in our work by means of measurement and following analysis of the polarized reflection spectra of the probe beam that allowed us to find a maximum Kerr rotation of 180 degrees in special point on detuning. As it follows from theoretical analysis, the main role in achievement of maximum Kerr rotation plays the asymmetry of the microcavity and the position of the impedance matching point but not the Q-factor of the microcavity.

Amphibians are animals that need two different kinds of habitats - water and forests - to achieve their life cycles. When water and forest are dissociated, their populations tend to decline. I present a simple population model based on diffusion equations aimed to get insight into this phenomenon. I show that there exists a critical split distance between the water and forest above which the population goes locally extinct.