In this series of talks, I would like to give a brief introduction to the theory of the hypoelliptic Laplacian developed by Bismut for symmetric spaces. This theory is a geometric approach to evaluate explici...

This talk is concerned with propagation dynamics for time-periodic partially degenerate reaction-diffusion systems with monostable nonlinearity. In the cooperative case, we prove the existence and expo...

This talk concerns the Fisher-KPP equation in a shifting environment. We are interested in the questions of whether such a forced moving KPP nonlinearity from behind can give rise to traveling waves with the same speed and how t...

When the propagation phenomena of reaction-diffusion models is considered, we always face to two questions: Can the propagation happen in every direction? Which direction is the propagation the fastest in? In this talk, we will intr...

In this talk we consider the nonnegative bounded solutions for reaction-advection-diffusion equations of the form $u_{t}-\Delta u+\alpha(t,y)u_{x}=f(t,y,u)$ in cylinders, where $f...

We study the moduli space of pairs consisting of a smooth cubic surface and a transverse plane via a period map.

In this talk, I first will introduce the linearized Energy stable and positivity preserving numerical scheme for solving Poisson-Nernst-Planck system, then provide energy stable numerical methods for solving charge transport Electrohydrodynamic (EHD) models with both Newtonian and non-Newtonian fluids. In particular, for Poisson-Nernst-Planck system, the spatial discretization is based on the reformulation of the Nernst-Planck equation, a three-level time stepping method is used to obtain the energy stability and ion concentration positivity preserving property.

Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic systems with N-peakon have been obtained, for instance, the DP equation, the Novikov equation, the Geng-Xue equation etc. In this talk, we will introduce the basic definition and some characters of peakon. Then some newly derived integrable dynamic systems with N-peakon will be presented. Meanwhile, new developments and hot points in the associated field are discussed.