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.

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.

Intersection cohomology is introduced by Goresky and MacPherson as a cohomogy theory on singular spaces which admit the Poincare duality. Decades of works show that this cohomology theory share a bunch of good properties such as Lefschetz package, Hodge-Riemann bilinear relation and Hodge theoretic purity. Although the theory is well established in the context of topology and algebra, the de Rham theorem remains open. In this talk I will introduce the basic knowledge of intersection cohomology and present a solution of the de Rham theorem for intersection cohomology when the space is algebraic and admits only equisingularities. This is the joint work with Chen Zhao.

Associated with a Coxeter group W, we may define a Hecke algebra H(W) and an endomorphism algebra E(W), called the Hecke endomorphism algebra. We use the defining relations for Hecke algebras to give a presentation for E(W) over a certain ring and speculate an extension to the integral case which is the key ingredients to categorify E(W) via singular Soergel bimodules.

We are going to recall the definition of partial entropy along expanding foliation, and its regularity with respect to maps