We study the gain in regularity of the distance to the boundary of a domain in $\mathbb R^m$. In particular, we show that if the signed distance function happens to be merely differentiable in a neighborhood of a …

In 1990 Le Gall showed an asymptotic expansion of the epsilon-neighborhood of a planar Brownian trajectory (Wiener sausage) into powers of 1/|log eps|, that involves the renormalized self-intersection local times. …

We consider a system of self-propelled agents that move at constant speed and control the curvature of their trajectories. This type of control provides a good fit to fish or bird trajectories. Trajectory control …

A classical problem in Nielsen theory concerns determining the minimum number of fixed points among all maps homotopic to a given continuous self-map f of a compact space. This problem motivated the definition of an …

Le théorème de Chevalley affirme que tout groupe algébrique lisse et connexe sur un corps parfait est extension d’une variété abélienne par un groupe affine lisse et connexe. Cela n’est plus vrai lorsque le corps de …

About higher degree skyrmions, based on https://arxiv.org/abs/2409.07205

Quid of the Jones polynomial A knot is a closed curve in 3d space. The basic problem in knot theory is to say whether two given knots can be deformed one into another. Knot invariants are efficient tools to answer …

les exposés du groupe de travail n'ont pas lieu en raison du grand nombre d'exposés du semestre Holomorphic Dynamics and Geometry of Surfaces (02/25 --> 06/25) https://indico.math.cnrs.fr/category/740/