Seminar of Geometry and its relatives
Student No.:10
Time:Thu 16:00-17:00, 2017.12.21
Instructor:Xu Guoyi, Huang Shaochuang  
Place:Conference room 1, Jin Chun Yuan West Building
Starting Date:2017-10-1
Ending Date:2017-12-22


Speaker: Mikhail Korobkov [Sobolev Institute of Mathematics, Russia and Fudan University, China]

Time: Thursday 16:00-17:00, 2017.12.21

Location: Conference room 1, Jin Chun Yuan West Building

Title: A bridge between Morse-Sard-Dubovitskii-Federer theorems and applications in fluid mechanics




Speaker: Deng Yuxing 邓宇星 [Beijing Normal University]

Time: Dec/14/2017 9:00am-10:00am

Location: Lecture Hall, Jin Chun Yuan West Building

Title: Higher dimensional steady Ricci solitons with linear curvature decay

Abstract: In this talk, we will talk about the rotational symmetry of gradient steady Ricci solitons with linear decay. Perelman conjectured that any 3d nonflat noncollapsed steady ricci solitons must be rotationally symmetric. This conjecture has been solved by Brendle around 2012. Recently, we generalize this result to noncollapsed steady Ricci solitons with nonnegative curvature operator in higher dimensions in addtion that the scalar curvature has linear decay. This is a joint work with Prof. Xiaohua Zhu.[arXiv:1710.07815]


Speaker: Zhang Yashan 张雅山 [Peking University]

Time: Dec/14/2017 10:15am-11:15am
Location: Lecture Hall, Jin Chun Yuan West Building

Title: Kaehler-Ricci flow with semi-ample canonical line bundle
Abstract: In this talk, we will first review some developments on the Kaehler-Ricci flow on compact Kaehler manifold with semi-ample canonical line bundle, focusing on the (weak) convergence to the generalized Kaehler-Einstein metric on the canonical model. Then we present the asymptotic near singular points of the generalized Kaehler-Einstein metric on a Riemann surface and some of its applications.




Speaker: Yin Hao 殷浩 [University of Science and Technology of China]
Time: Dec/14/2017 1:30pm-2:30pm
Location: Lecture Hall, Jin Chun Yuan West Building

Title: Schauder estimate on smooth and singular spaces

Abstract: In this talk, we present a (maybe) new point of view on the classical Schauder estimate. Following this line, we discuss an estimate that could be regarded as the counter part of Schauder estimate on singular spaces (with cone-like singularities).


Speaker: Guo Hongxin 郭洪欣 [Wenzhou University]

Time: Dec/14/2017 2:45pm-3:45pm
Location: Lecture Hall, Jin Chun Yuan West Building

Title: Constructing monotone quantities in geometric flows via the Boltzmann entropy

Abstract: In this talk we shall present a method to construct monotone geometric quantities in geometric flows by studying the classical Boltzmann entropy.



Speaker: Lee Man-Chun 李文俊 [The Chinese University of Hong Kong]

Time: Dec/14/2017 4:00pm-5:00pm
Location: Lecture Hall, Jin Chun Yuan West Building

Title: Chern-Ricci flow on non-compact manifolds with applications

Abstract: In this work, we study geometric flow of metrics along the direction of Chern-Ricci curvature. We obtain an existence criteria for Chern-Ricci flow on non-compact manifolds. Using this, we study the Ricci flow on non-collapsing Kaehler manifolds with non-negative bisectional curvature and give an alternative proof of Gang Liu's result on Yau's uniformization conjecture. This is joint work with Prof. L.-F. Tam.





Speaker: Renjie Feng 冯仁杰 [Peking University]
Time: Nov/09/2017 1:30pm-2:30pm
Location: Jing Zhai 304

Title: Spectrum of SYK model
Abstract: We will study the spectral properties of the random matrix of SYK model, which is a simple model of the black hole in physics literature. We will show the global statistics of the expected density of the eigenvalues as the number of Majorana fermions tends to infinity. We will discuss some open questions, such as local statistics of first eigenvalues.



Speaker: Fei He 贺飞 [Xiamen University]
Time: Nov/09/2017 2:45pm-3:45pm
Location: Jing Zhai 304

Title: Existence of Ricci flow on manifolds with unbounded curvature
Abstract: The existence of Ricci flow on manifolds with unbounded curvature is an interesting problem which is still not well-understood. I will talk about some recent progress on this problem, and show a few immediate applications of these Ricci flow solutions.



Speaker: Huichi Huang 黄辉斥 [Chongqing University]
Time: Nov/09/2017 4:00pm-5:00pm
Location: Jing Zhai 304

Title: Fourier coefficients of $\times p$-invariant measures on the unit circle
Abstract: To study Fourier coefficients of $\times p$-invariant Borel probability measures on the unit circle, we obtain two results. On one hand, we prove a measure rigidity result under actions of multiplicative sub-semigroups of $\mathbb{N}$. On the other hand, we prove a Wiener-type theorem for compact metrizable groups whose proof relies on a generalized mean ergodic theorem for amenable discrete quantum groups.






Speaker: Hua Bobo 华波波 [Fudan University]
Title: Hausdorff dimension of a set
Abstract: In this talk, we review some methods estimating the Hausdorff dimension of a set.


Speaker: Lai Mijia 来米加 [Shanghai Jiao Tong University]
Title: On isoperimetric problem; on Yamabe constant and sigma invariant.
Abstract: As the title suggests, I mainly talk about two subjects. 
In the first two talks, I will survey some results on isoperimetric problem. In the third lecture, I will discuss Bray-Neves's work on 
sigma invariant and some related works. In the last talk, I will present a recent work joint with Xuezhang Chen and Fang Wang on conformally compact Einstein manifolds. 


Speaker: Li Yi 李逸 [Universite du Luxembourg]
Title: Ricci-harmonic flow and Einstein's equations
Abstract: In the first three talks, we will discuss the basic properties of Ricci-harmonic flow (RHF) and Einstein's equations (EE). A recent work on  RHF/EE will be presented at the last talk. 


Speaker: Wang Zuoqin 王作勤 [USTC]
Title: Upper bounds of small eigenvalues
Abstract: Given a closed manifold $M$. Consider all Riemannian metrics on $M$ that has fixed volume. Which metric maximize the first eigenvalues of the Laplace-Beltrami operator? In this series of talks, I will try to summarize known results on this problem.  


Oct 1st: 
9:30-10:30am    Wang Zuoqin,
10:45-11:45am  Hua Bobo,
2:30-3:30pm       Lai Mijia, 
3:45-4:45pm       Li Yi,

Oct 2nd: 
9:30-10:30am    Hua Bobo,
10:45-11:45am  Lai Mijia, 
2:30-3:30pm      Li Yi,
3:45-4:45pm      Wang Zuoqin,

Oct 3rd: 
9:30-10:30am     Lai Mijia, 
10:45-11:45am   Li Yi,
2:30-3:30pm       Wang Zuoqin,
3:45-4:45pm       Hua Bobo,

Oct 4th: 
9:30-10:30am     Li Yi,
10:45-11:45am  Wang Zuoqin,
2:30-3:30pm       Hua Bobo,
3:45-4:45pm       Lai Mijia,