In this talk, we will study C^{1, 1} regularity for solutions to the degenerate Lp Dual Minkowski problem and the existence of the smooth solution to the Gauss image.腾讯会议号：131-965-267会议链接：https://meeting.tencent.com/dm/iD9IGmFJEu19 All are ...

In this talk, by using new auxiliary functions, we study a class of contracting flows of closed, star-shaped hypersurfaces in R^n+1 with speed $r^{\frac{\alpha}{\beta}} \sigma_k^{\frac{1}{\beta}}$, where $\sigma_k$ is the $k$-th element...

In this talk, we will first introduce some classical topics concerning the geometry of minimal surfaces in R^n. Then we will discuss the Bernstein type theorems and Gauss-Bonnet type formula for minimal surfaces in R^3 or R^n...

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.

Mean curvature is one of the most fundamental extrinsic curvature in the theory of submanifold. A natural question is that wether mean curvature can control the area of hypersurfaces. In this talk, we discuss the area comparison with respect to mean curvature for hypersurfaces in space forms. This is a joint work with Professor Sun Jun in Wuhan University.

We study the moduli space of pairs consisting of a smooth cubic surface and a transverse plane via a period map. More specifically, the construction associates to a cubic surface pair a so-called Eckardt cubic threefold which admits an involution, and the period map sends the pair to the anti-invariant part of the intermediate Jacobian. Our main result is that the global Torelli theorem holds for the period map (in other words, the period map is injective). The key ingredients of the proof include a description of the anti-invariant part of the intermediate Jacobian as a Prym variety of a branched cover and a detailed study of certain positive dimensional fibers of the corresponding Prym map. This is joint work with S. Casalaina-Martin.

We are concerned with a system of equations governing the evolution of isothermal, viscous and capillary compressible fluids, which is used as the phase transition model. In the case of zero sound speed, it is found that the linearized system admits a purely parabolic structure. Consequently, one can establish the global-in-time existence and Gevrey analyticity of Lp solutions in hybrid Besov spaces, which improves the prior L2 bounds on the low frequencies of density and velocity due to acoustic waves. The proof mainly relies on new Besov (-Gevrey) estimates for product and composition of functions.

在这个数据科学越来越受到重视，数据越来越受到重视的今天，数据的科学治理与合规使用，也变得越来越重要。本次报告，围绕以下几个方面：第一、目前我们看到的数据合规案例和问题有哪些。第二、目前我国同数据合规使用相关的法律条文有哪些。第三、在过去的这些年里，同数据相关的司法诉讼经典案例，做有挑选的探讨。最后，对我国数据合规使用有指导性的基本原则做了总结。