# Monotonic-friendly diffusions (Baptiste Huguet, Institut de Mathématiques de Bordeaux)

04.03.2019 17:00

We study semi-group $\mathbf{P}_t$ with generator $\frac{1}{2}\Delta + \nabla V.\nabla$ on Riemannian manifold, acting on smooth functions. We are looking for conditions on the potential $V$ so that the semi-group preserves the monotonicity of functions. If the question is kind of natural in the Euclidean case, the concept of monotonicity has to be discussed in manifolds . I will present the results in $\R^n$ and in a class of very sweet manifolds : Lie groups. This will be an excuse to introduce some probabilistic (diffusion, stochastic equation...) and geometric (connection, parallel translation) tools in a cosy way.

### Lieu

Room 17, Séminaire des doctorants

### Organisé par

Section de mathématiques

### Intervenants

Baptiste Huguet, Institut de Mathématiques de Bordeaux

entrée libre

### Classement

Catégorie: Séminaire