Laboratoire de Mathématiques Jean Leray

Fully spectral scheme for the linear BGK equation on the whole space.

In this article, we design a spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass and energy conservation. We focus on the linear BGK equation with a confining potential Φ, even if the method could be applied to different collision oper...

Every negative amphichiral knot is rationally slice

In 2009, Kawauchi proved that every strongly negative amphichiral knot is rationally slice. However, as shown by Hartley in 1980, there are examples of negative amphichiral knots that are not strongly negative amphichiral. In this paper, we prove that every negative amphichiral l...

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

We consider the non-selfadjoint, semiclassical Schrödinger operator \mathscr{L}(h) := -h^{2}\partial_{x}^{2}+e^{i\alpha}V , where \alpha \in (-\pi,\pi) and V\colon \R\to \R_{+} is even and vanishes at exactly two (symmetric) non-degenerate minima. We establish a semiclassical tun...