## 3 événements

• Séminaire de lecture M2 Maths Pures

### Lundi 23 octobre 2017 10:00-12:00 - Yulieth Prieto

Connections on vector bundles

Résumé : In this talk, we will introduce the role of a covariant derivative (or linear connection) $\nabla$ of a smooth vector bundle which will be important to define the parallel transport on fibers. One of the crucial facts here is the definition of a moving frame and the matrix-valued 1-form associated to the linear connection in local coordinates of a section. A natural extension of $\nabla$ will be associate an exterior derivative $d^\nabla$, and will give a notion of a curvature in this context. We will see that this curvature measures the holonomy of $\nabla$. Also, we will describe one remarkable algebraic feature of the curvature by the Bianchi identity. We finish with a description of the linear connection in the particular case of the tangent bundle.

Lieu : Salle Picard

• Séminaire doctorants Picard

### Lundi 23 octobre 2017 13:30-14:30 - Jean-Marc Hok

C’est quoi le polynôme de HOMFLYPT ?

Résumé : On commencera par une brève introduction à la théorie des nœuds pour les non initiés avant de présenter le polynôme de HOMFLY-PT et diverses façons de la calculer (Algorithme de diagrammes descendants et modèle d’états de Jaeger).

Lieu : Salle Picard (129 1R2)

• Séminaire d’Analyse Réelle

### Lundi 23 octobre 2017 16:00-17:15 - Andre Schlichting - Université de Bonn

A non-local Fokker-Planck equation related to nucleation and coarsening

Résumé : In this talk we consider a Fokker-Planck equation modeling nucleation and coarsening of clusters very similar to the classical Becker-Döring equation.
The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. In this way the equation has formally the structure of a McKean-Vlasov equation, but with a non-local boundary condition.
We briefly discuss the well-posedness and regularity properties of the Cauchy-Problem. Here the main difficulty is to improve basic a priori regularity properties of the non-local order parameter.
The main part of the talk focuses on the longtime behaviour of the system. The system posses a free energy, whch strictly decreases along the evolution and leads to a gradient structure involving boundary conditions.
We generalize the standard entropy method based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates. In this way, we obtain an explicit characterization of the convergence to equilibrium with algebraic or even exponential rates depending on the particular assumptions on the vector fields, diffusivity and initial data.
(joint work with J. Conlon)

Lieu : Bâtiment 1R1, salle 106