Advanced PDE Seminars
“偏微分方程前沿讨论班”旨在为国内偏微分方程领域青年教师和学生开设学科前沿课程，促进彼此间的交流和合作，已成功举办三届。前三届分别在浙江大学，中国科学技术大学，中科院数学所举办。第四届“偏微分方程前沿讨论班”将于2019年5月19日6月1日在浙江大学举办，这些课程将主要聚焦于椭圆和抛物型方程，与几何分析也联系密切，预计有80位青年教师和学生参加。
Advanced PDE Seminars aims to provide cuttingedge courses in partial differential equations for young scholars and students in China, and promote exchanges and cooperation between them. The Seminars have been successfully held for three years in Zhejiang University（Hangzhou, 2016）, University of Science and Technology of China(Hefei,2015) , Academy of Mathematics and Systems Science , Chinese Academy of Sciences (Beijing, 2014) respectively. The fourth Advanced PDE Seminars will be held in the School of Mathematical Sciences, Zhejiang University from May 19th to June 1st, 2019.The courses will focus on elliptic and parabolic equations, and have a strong favor of "geometric analysis". About 80 young scholars and students will attend the seminar.
Place:
Lecture hall in Institute of Advanced Mathematics, East 7 Building, Zijingang Campus, Zhejiang University, Hangzhou.
(浙江大学紫金港校区东7数学高等研究院报告厅)
Topics:
Nonlocal Elliptic and Parabolic Equations and Free Boundary Problems.
Committee:
Fanghua Lin (New York Uniersity)
Xinan Ma (University of Science and Technology of China)
Weimin Sheng (Zhejiang Uniersity)
Wei Wang (Zhejiang Uniersity)
Ting Zhang (Zhejiang Uniersity)
1. Dennis Kriventsov (Rutgers University)
2. Fanghua Lin (New York Uniersity)
3. Joaquim Serra (ETHZurich),
4. Yannick Sire (John Hopkins University),
5. Kelei Wang (Wuhan University)
6. JunCheng Wei (University of British Columbia)
Dennis Kriventsov:
Title: Regularity of Free Boundaries via Linearization
Abstract: While the structure of free boundaries in Bernoulli and obstacletype problems is potentially quite complicated, the fact remains that at generic points, one expects that the interface is smooth and wellapproximated by some simple onedimensional profile. An observation of De Giorgi, in his work on minimal surfaces, was that this is a great setup for a compactness argument which essentially reduces it to studying a linearized problem for smooth perturbations of the tangent object. We will discuss how the same insight can be applied to Bernoulli problems, following a work of De Silva. Time permitting, we will also consider some further recent extensions by the speaker and F. Lin, other free boundary problems which can be tackled, and the case of the obstacle problem.
Yannick Sire:
Title:Asymptotics for nonlocal geometric equations and applications
Abstract:The aim of the lectures is to develop tools in Geometric Measure Theory and calculus of variations to study geometric problem which are of nonlocal nature such as harmonic maps with free boundary and minimal surfaces with free boundary. We will investigate mainly two problems in singular perturbation theory: the fractional GinzburgLandau system and the fractional AllenCahn equation. Each of those exhibit nonlocal phenomena and new approaches have to be developed to deal with the limit.
1 Basic theory of standard Minimal Surfaces
2 Basic theory of standard Harmonic maps
3 Fractional harmonic maps and their extension as harmonic maps with free boundary
4 Nonlocal minimal surfaces
5 The half GinzburgLandau system
6 The fractional AllenCahn equation
7 Elements of parabolic theory
Joaquim Serra:
Title: THE OBSTACLE PROBLEM: REGULARITY OF THE FREE BOUNDARY AND ANALYSIS OF SINGULARITIES
Abstract: The classical obstacle problem can be seen as the paradigm of free boundary problems. It is equivalent, after certain transformations, to other wellknown free boundary problems such as the Stefan problem. We will give an introduction to the regularity theory for the free boundary of the obstacle problem. We will revisit the classical theory (with some new proofs) and also explain some recent exciting developments on the analysis of singularities.
Kelei Wang:
Title: Second order estimates on transition layers
Abstract: I will discuss a second order regularity theory on level sets of solutions to the singularly perturbed AllenCahn equation, established recently with Juncheng Wei. The main foucus of the lectures will be devoted to the derivation of Toda system from AllenCahn equation, by using the infinite dimensional Lyapunov–Schmidt reduction method devloped by M. del Pino, M. Kowalczyk and Juncheng Wei. If time permits, I will also discuss some applications of this second order regularity theory, including the classification of finite Morse index solutions of AllenCahn equation, a proof of the multiplicity one conjecture of Marques and Neves by Chodosh and Mantoulidis using AllenCahn approximation.
Juncheng wei:
Title: Parabolic gluing method and finite time singularity for twodimensional nematic liquid crystal flow
Abstract: I will introduce recently developed parabolic gluing methods and its application to construction of finite time blowup to twodimensional nematic liquid crystals flows introduced by C. Liu and F. Lin.
TBA..
Schedule:
注册：14:0020:00, May 19, 2019, Lobby in Zijingang International Hotel (紫金港国际饭店)
Date 
Time 
Speakers 
May 20 (Monday) 
9:0010:00& 10:2011:20 
Yannick Sire 

Free 

May 21 (Tuesday) 
9:0010:00& 10:2011:20 
Yannick Sire 
14:0015:20 & 15:4017:00 
Kelei Wang 

May 22 (Wednesday) 
9:0010:00& 10:2011:20 
Yannick Sire 
14:0015:20 & 15:4017:00 
Kelei Wang 

May 23 (Thursday) 
9:0010:00& 10:2011:20 
Yannick Sire 
14:0015:20 & 15:4017:00 
Kelei Wang 

May 24 (Friday) 
9:0010:00& 10:2011:20 
Juncheng Wei 
14:0017:00 workshop 


May25(Saturday) 
9:0011:30 workshop 

14:0017:00 workshop 


May 27 (Monday) 
9:0010:00& 10:2011:20 
Joaquim Serra 
14:0015:00 & 15:2016:20 
Dennis Kriventsov 

May 28 (Tuesday) 
9:0010:00& 10:2011:20 
Joaquim Serra 
14:0015:00 & 15:2016:20 
Dennis Kriventsov 

May 29 (Wednesday) 
9:0010:00& 10:2011:20 
Joaquim Serra 
14:0015:00 & 15:2016:20 
Dennis Kriventsov 

9:0010:00& 10:2011:20 
Joaquim Serra 

14:0015:00 & 15:2016:20 
Dennis Kriventsov 

May 31 (Friday) 
9:0010:00& 10:2011:20 
Fanghua Lin 
Zijingang International Hotel, 796 Shenhua Road, Hangzhou
(紫金港国际饭店, 申花路796号)
http://hzzijinganginternationalhotel.vip.lechengol.com/
We could support 40 young researchers and Ph.D students' accommodations during the period, (2 person share one Standard Room)
Email: APDES2019@163.com
Zhejiang University
University of Science and Technology of China
TianYuan Foundation of NSFC
NSFC
主办单位：浙江大学数学科学学院，浙江大学数学高等研究院，中国科学技术大学，浙江紫金港国际饭店
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