We solve the Gursky-Streets equations with uniform C^1,1 estimates for . An important new ingredient is to show the concavity of the operator which holds for all . Our proof of the concavity heavily relies on Garding's theory of hyperbolic polynomials and results from the theory of real roots for (interlacing) polynomials. Together with this concavity, we are able to solve the equation with the uniform C^1,1 a priori estimates for all the cases . Moreover, we establish the uniqueness of the solution to the degenerate equations for the first time.

We shall first give a brief introduction for Alexandrov geometry, which is a class of singular metric spaces with curvature bounded from below by triangle comparisons, and then we introduce a result about regularity of harmonic maps from an Alexandrov space to a compact Riemannian manifold, which is based on the joint works with Prof. Huabin Ge and Prof. Wenshuai Jiang.

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.

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。 最后，我们将简要介绍报告人在素数变量二次形上的一些工作

题目：Average Bounds Toward the Generalzied Ramanujan Conjecture报告人：王英男 副教授 （深圳大学）地点：腾讯会议室时间：2020 年 05 月12 日 09:00-10:00摘要：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.点击链接入会，或添加至会议列表：https://meeting.tencent.com/s/5gXpEDI2d01c会议...

It is well-known that there is only one compact Kahler manifold with zero first Chern class up to diffeomorphism in complex dimension 1. This is topologically a torus and is an example of Calabi-Yau manifold. The Ricci-flat metric on a torus is actually a flat metric. In dimension 2, the K3 surfaces furnish the compact simply-connected Calabi-Yau manifolds. However in 3 dimension, it is an open problem whether or not the number of topologically distinct types of Calabi-Yau 3-folds is bounded. From the view point of physics (String theory), S.T. Yau speculates that there is a finite number of families of Calabi-Yau 3-folds.