时间：2021年12月11日-2021年12月13日 8:00-21:00

Time：8:00-21:00, December 11, 2021 - December 13, 2021

地点：西湖大学云栖校区4号楼409-411教室

Venue: Room 409-411, Building 4, Yunqi Campus, Westlake University

线上：腾讯会议ID：317-2637-8510, 密码：1112

Online: Tencent Meetings ID: 317-2637-8510, Password: 1112

本次会议将采取线上与线下相结合的方式举行，杭州本地参加者可以线下参加会议。

组织者：王友德教授，李宇翔教授和赵永强

Organizers: Prof. Youde Wang, Prof. Yuxiang Li & Yongqiang Zhao

特邀演讲人/Invited Speakers:

Youde Wang   Guangzhou University & Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Chong Song    Xiamen University

Yong Luo       Chongqing University of Technology

Hao Yin        University of Science and Technology of China

Haozhao Li     University of Science and Technology of China

Guodong Wei   Zhuhai Campus of Sun Yat-Sen University

Ning Jiang      Wuhan University

Lifeng Zhao     University of Science and Technology of China

Jun Yang        Guangzhou University

Kai Zheng       Tongji University

Yalong Shi       Nanjing University

Zongming Guo  Henan Normal University

日程/Schedule:

1、主讲嘉宾/Speaker：Prof. Youde Wang, Guangzhou University & Academy of Mathematics and Systems Science, Chinese Academy of Sciences

主讲题目/Title：Recent progress on the Schrodinger flow

摘要/Abstract:

    In this talk, we will introduce some recent results on the Schrodinger flow and related models. In particular, we will review well-posedness theory and dynamical behaviors for both initial value problem and initial-boundary value problem.

2、主讲嘉宾/Speaker：Prof. Chong Song, Xiamen University

主讲题目/Title：Skew Mean Curvature Flow

摘要/Abstract:

    The Skew Mean Curvature Flow (SMCF), which describes the evolution of a codimension two submanifold along its binormal direction, is a Schrodinger-type quasi-linear PDE system and naturally generalizes the famous vortex filament equation. In this talk, I will first introduce the background and recent progress of SMCF, and then present a proof of the local well-posedness of the SMCF for general dimensional closed submanifolds in Euclidean spaces.

3、主讲嘉宾/Speaker：Prof. Yong Luo, Chongqing University of Technology

主讲题目/Title： Rigidity of CSL submanifolds in the unit sphere

摘要/Abstract:

    A contact stationary Legendrian submanifold (briefly, CSL submanifold) is a stationary point of the volume functional of Legendrian submanifolds in a Sasakian manifold. In this talk we will discuss pinching phenomena of CSL submanifolds in the unit sphere. Actually, we will show that if the square length of the second fundamental form of a CSL submanifold in the unit sphere belongs to, where is a positive number depending on the n and the mean curvature vector filed, then it must be totally geodesic, minimal or a Calabi product. This is a recent joint work with Linlin Sun.

4、主讲嘉宾/Speaker：Prof. Hao Yin, University of Science and Technology of China

主讲题目/Title：Smoothing estimate for Logrithmic Fast Diffusion equation and Ricci flow on surfaces

摘要/Abstract:

    In this talk we discuss a few smoothing estimates for the logrithmic fast diffusion equations. As applications, we study a Ricci flow solution on surface with very rough initial data.

5、主讲嘉宾/Speaker：Prof. Haozhao Li, University of Science and Technology of China

主讲题目/Title：Stable minimal hypersurfaces in R⁴

摘要/Abstract:

    In this talk, I will present the work by Otis Chodosh and Chao Li that a complete, two-sided, stable minimal immersed hypersurface in R⁴ is flat.

6、主讲嘉宾/Speaker：Prof. Guodong Wei, Zhuhai Campus of Sun Yat-Sen University

主讲题目/Title：On the minimizers of curvature functionals in asymptotically flat manifolds

摘要/Abstract:

In this talk, we will discuss the minimizers of curvature functionals (Willmore functional and extrinsic energy functional) subject to an area constraint in asymptotically flat manifolds. Under some certain conditions, we prove such minimizers exist.

7、主讲嘉宾/Speaker：Prof. Ning Jiang, Wuhan University

主讲题目/Title：On inertial Ericksen-Leslie system for nematic liquid crystals

摘要/Abstract:

    In this talk, we will review recent progress on the analytic studies on the inertial Ericksen-Leslie system for nematic liquid crystals. This system is a coupling of Navier-Stokes equations and wave map (the target manifold is 2-sphere) type equations. We study the well-posedness in the context of regular solutions, and justify the zero-inertia limit to the corresponding parabolic Ericksen-Leslie system. We also consider other asymptotic analysis problem, such as low Mach number limit, and dissipative solutions.

8、主讲嘉宾/Speaker：Prof. Lifeng Zhao, University of Science and Technology of China

主讲题目/Title：：Blowup dynamics for smooth equivariant solutions to energy critical LandauLifschitz flow

摘要/Abstract:

    We study the energy critical equivariant Landau-Lifschitz flow with target manifold S². We prove that there exists a codimension one smooth well-localized set of initial data which generates finite-time type-II blowup solutions, and then give a precise description of the corresponding singularity formation. In our proof, both the Schrodinger part and the heat part play important roles in the construction of approximate solutions and the mixed Energy-Morawetz arguments. However, the blowup rate is independent of their coefffficients. This talk is based on the joint work with Jitao Xu.

9、主讲嘉宾/Speaker：Prof. Jun Yang, Guangzhou University

主讲题目/Title：Construction of interface solutions by reduction method

摘要/Abstract:

We will review some results on the construction of interface solutions fo some nonlinear equations and then discuss some problems under working. Besides some delicate techniques in analysis, the construction relies on the variational properties of minimal surfaces or Willmore surfaces in differential geometry.

10、主讲嘉宾/Speaker：Prof. Kai Zheng, Tongji University

主讲题目/Title：On degenerate cscK metric

摘要/Abstract:

    In this talk, we will present results on degenerate cscK metric. We will start with its construction and then continue to show its geometric applications.

11、主讲嘉宾/Speaker：Prof. Yalong Shi, Nanjing University

主讲题目/Title：Constant scalar curvature Kahler metrics on ramified Galois covers

摘要/Abstract:

    Let f : M → N be a finite ramified Galois cover between compact Kahler manifolds. If N has a cscK metric, under suitable conditions, we shall prove the existence of cscK metrics on M. This generalizes previous works of Arezzo-Ghigi Pirola and Li-Sun on Kahler-Einstein metrics. This is joint work with Claudio Arezzo and Alberto Della Vedova.

12、主讲嘉宾/Speaker：Prof. Zongming Guo, Henan Normal University

主讲题目/Title：Non-radial singular solutions for some elliptic equations

摘要/Abstract:

Non-radial singular solutions for a class of elliptic equations are constructed. Detailed asymptotic behaviors at the isolated singular point of prescribed singular solutions for the equations play an important role in the construction. Asymptotic expansions up to arbitrary orders at the isolated singular point of prescribed singular solutions are established. Infinitely many non-radial singular solutions for the equations are constructed in the forms given in the asymptotic expansions via introducing suitable weighted Holder spaces related to the operators of the equations.

讲座联系人/Contact:

理学院 王老师  wangqiuhui@westlake.edu.cn