We study the dynamics of reaction-diffusion-advection models for single and two competing species in one-dimensional periodic habitats, where the individuals are subject to both diffusion and advection. We establish the monotone dependence of the principal eigenvalue on diffusion and drift rates. As applications, we first consider the persistence and spatial spreading of a single species and establish the critical threshold for the persistence as well as the monotone dependence of the minimal wave speed on the drift rate. We also consider two competing species model and study the local and global stability of semi-trivial steady states. Furthermore, the existence of evolutionarily singular strategies is established, which helps gain deeper insight into the evolution of dispersal in advective environments. This is a joint work with Shuang Liu.

In this talk I will consider the Fisher-KPP equation on the half line with Dirichlet boundary condition. We will construct some entire solutions for this problem. Each of them has different alpha-limit as the time goes to minus infinity. and can be used to characterize the asymptotic behavior for different initial data.

几何流也叫几何发展方程，是指关于某些几何量的演化方程。按照这些几何量的属性，几何流可以分为内蕴几何流与外蕴几何流。内蕴几何流以Ricci流为代表，外蕴几何流以平均曲率流为代表。我们将简要回顾几何流，特别是Ricci流和平均曲率流的发展历程、当前状况、以及其可能的应用前景。

In this talk we will show that the volume of compact Kahler manifold with positive Ricci curvature cannot be bigger than the volume of the complex projective space. The proof requires some construction from convex geometry that goes back to Okounkov. The entire argument is purely algebraic and is quite different from the analogous Bishop's sphere theorem in Riemannian geometry.

In this talk, we present the asymptotic behavior of the solutions for the out-flow problem to the one-dimensional compressible Navier-Stokes-Poisson equation. First, we construct the nonlinear wave, then we address the large-time behavior of the solution by energy method. This is a joint work with Prof. Peicheng Zhu.

Let M be an m dimensional closed Kaehler manifold. We will present certain eigenvalue and heat kernel estimates for the Hodge Laplacian acting on smooth sections of the canonical bundle of M, i.e., (m,0)-forms. The main results only rely on the bound of the Ricci curvature, and the volume and diameter of M, instead of the bound of the whole curvature tensor for general differential forms.

Recently, an Orlicz Aleksandrov problem has been posed and two existence results of solutions to this problem for symmetric measures have been established. In this talk, we will report the existence and uniqueness of solutions to the Orlicz Aleksandrov problem for non-symmetric measures.

I will talk about the rigidity of contact stationary Legendrian (CSL) submanifolds in the unit sphere based on the joint works with Prof. Luo Yong and Dr. Yin Jiabin.