In this talk, I first introduce mean curvature flow briefly, and then mainly consider closed hypersurfaces immersed in a space of constant sectional curvature evolving in direction of its outer unit normal vector with speed given by a general curvature function of principal curvatures, such that the initial hypersurface is pinched in the sense that the ratio of the biggest and smallest principal curvatures of the hypersurface is close enough to 1 everywhere. We prove that the pinching is preserved as long as the flow exists, and the flow shrinks to a point in finite time. Especially, if the speed is a high order homogeneous function, the normalized flow exists for all time and converges smoothly and exponentially to a round sphere in Euclidean space.

In this talk, I will present a preliminary report of a problem asked by Vitali Milman. This is if there are two convex bodies K and L such that $K+L=K^o+L^o$, is it true that $K=L^o$?

By using Seshadri constants for subschemes, we establish a second main theorem of Nevanlinna theory for holomorphic curves intersecting subschemes in (weak) subgeneral position. We also give the corresponding Schmidt's subspace theorem in Diophantine approximation.

The generalized Ramanujan conjecture (GRC) for Maass forms is still open. In this talk we will survey the recent results and developments centered on this problem.

素数变量的丢番图方程的研究历史悠久。研究方法涉及圆法，筛法和指数和等重要解析数论方法。本报告，将综述关于素数变量丢番图方程的一些研究内容，方法以及最新的进展。

本报告试图通过一些观点和例子谈一谈怎样理解数学，如什么样的东西是基本的，什么样的问题是好问题，数学美的含义，如何理解数学的思维方式等。

The existence of Kahler Einstein metric with mixed cone and cusp singularity has attracted many attentions in recent years. In this talk, we show that their L2 cohomologies coincide with the de Rham cohomology of a good compactification (under both Dirichlet and Neumann boundary conditions) and prove that their L2-Hodge -Frolicher spectral sequence give the pure Hodge structure on them. This is a work joint with Junchao Shentu.