Download Workshop on Spectral Geometry General Information

Handbook of Workshop:
Spectral Geometry
December 22-23, 2016
Workshop on Spectral Geometry
General Information:
The aim of the workshop is to bring together experts in spectral geometry
to discuss recent progress on related topics.
Workshop Location:
Room 2201, Guanghua East Building (main), Fudan University
Speakers:
 Hua Chen,
Wuhan University
 Xianzhe Dai,
UC Santa Barbara
 Xiaolong Han,
California State University, Northridge
 Shiping Liu,
University of Science and Technology of China
 Fanghua Lin,
to be confirmed
 Zhiqin Lu,
UC Irvine
 Fang Wang,
Shanghai Jiaotong University
 Fengyu Wang,
Beijing Normal University
 Wenjiao Yan,
Beijing Normal University
 Jialin Zhu,
Shanghai Center for Mathematical Sciences
 Miaomiao Zhu,
Shanghai Jiaotong University
Scientific Committee:
Jixiang Fu, Jiaxing Hong, Xinan Ma, Jiayu Li
Organizers:
Bobo Hua: [email protected]
Zuoqin Wang: [email protected]
Sponsors:
School of Mathematical Sciences, Fudan University
Shanghai Center for Mathematical Sciences, Fudan University
Workshop secretaries:
Huihui Chen: [email protected]
Jiacheng Huang: [email protected]
Yan Huang: [email protected]
Transportation:
How to get to Fudan?
There are three choices from Pudong Airport (PVG) to Fudan University:
 Take taxi (about 50 minutes, about 170 RMB).
 Take Maglev Speed Train to Long Yang Road Station (50 RMB), then
take taxi (about 60 RMB).
 Take Airport Bus Line 4, get off at Wu Jiao Chang Station (20 RMB).
Then walk about 10 minutes.
 Take Shanghai metro line No. 2 to Guanglan Road, get off and take again No.
2 (the one to city center) to Nanjing East Road, transfer to No. 10, get off at
Jiangwan Stadium Station. Then walk about 10 minutes.
There are two choices from Hongqiao Airport (SHA) to Fudan University:
 Take taxi (about 95 RMB).
 Take Shanghai metro line No. 10 to Jiangwan Stadium Station (5 RMB).
Then walk about 10 minutes.
From Shanghai Railway Station to Fudan University:
 Exit at the North Exit, then take Bus No. 942 to Fudan University. Or take
taxi (about 40 RMB).
From Shanghai South Railway Station to Fudan University:
 Take Shanghai metro line No. 3 to DaBaiShu Station, then take taxi (about 14
RMB) or take Bus No. 133 to Fudan Universtiy. Or take taxi (about 95 RMB).
Further information
The following links point to pages that contain more information about Shanghai:
 Shanghai China
 Shanghai Travel Guide
Schedule：
For addresses of Restaurants, please see the last page of the handbook.
Titles and Abstracts:
1. Xianzhe Dai,
UC Santa Barbara
Title: An eigenvalue problem for manifolds with conical singularities
Abstract: Perelman's entropy functional plays an important role in analyzing Ricci
flow. We develop Perelman's entropy functional for manifolds with conical singularity.
It involves an eigenvalue problem for a singular Schrodinger operator and the analysis
of the asymptotic behavior of its eigenfunctions near the conical singularity. This is
joint work with Changliang Wang.
2. Hua Chen,
Wuhan University
Title：Estimates of eigenvalues for a class of bi-subelliptic operators
Abstratct：Let $X = (X_1, X_2, \cdots, X_m)$ be a system of real smooth vector fields
defined on a bounded open domain $\Omega\subset \mathbb{R}^n$ with smooth
boundary $\partial\Omega$ which is non-characteristic for $X$. If $X$ satisfies the
Hormander's condition, then the vector fields is finitely degenerate and the sum of
square operator $\triangle_{X}=\sum_{j=1}^{m}X_j^2$ is a subelliptic operator. In
this talk, let $\lambda_{k}$ be the $k$-th Dirichlet eigenvalue for the bi-subelliptic
operator $\triangle_{X}^2$ on $\Omega$, we shall use the subelliptic estimates to give
the explicit lower bounds of $\lambda_{k}$, which is the extension of the classical
result for bi-harmonic operator.
3. Fengyu Wang,
Title:
Beijing Normal University
Coupling by change of measure and applications
Abstract: The classical Harnack inequality has been widely applied in PDEs and
Geometry Analysis. However, as the inequality is essentially depend on the dimension
of generator, it is invalid for infinite-dimensional models. To establish infinitedimensional Harnack inequalities, we introduce a new coupling method by change of
measures, which allow the coupling to be successful at given fixed time. By looking at
a simple stochastic differential equation, we explain the idea for applications of this
method to the study of Harnack inequality, Bismut derivative formula and integration
by parts formulas for Markov semigroups.
4. Jialin Zhu,
Title:
Shanghai Center for Mathematical Sciences
Scattering matrix and analytic torsion
Abstract: For a compact manifold, which has a part isometric to a cylinder of finite
length, we consider an adiabatic limit procedure, in which the length of the cylinder
tends to infinity. We study the asymptotic of the spectrum of Hodge-Laplacian and
the asymptotic of the L^{2}-metric on de Rham cohomology. As an application, we
give a pure analytic proof of the gluing formula for analytic torsion. (joint work with
Martin Puchol and Yeping Zhang)
5. Genqian Liu,
Beijing Institute of Technology
Title: Sharp higher-order Sobolev inequalities in the hyperbolic space
Abstract: In this talk, we give the sharp k-th order Sobolev inequalities in the
hyperbolic space for all positive integer k. This gives an answer to an open question
raised by Aubin in [Aubin, Princeton University Press, Princeton (1982), pp. 176–177].
In addition, we prove that the associated Sobolev constants are optimal.
6. Shiping Liu,
University of Science and Technology of China
Title: Ricci curvature and eigenvalue estimates for discrete and continuous magnetic
Laplacian
Abstract: We present Lichnerowicz type estimates and (higher order) Buser type
estimates for the magnetic Laplacian on discrete graphs with signatures and on closed
Riemannian manifolds with magnetic potentials. These results relate eigenvalues,
magnetic fields, Ricci curvature and Cheeger type constants. This is based on joint
work with Michela Egidi, Florentin M\"unch, and Norbert Peyerimhoff.
7. Wenjiao Yan,
Beijing Normal University
Title: Isoparametric foliation and the first eigenvalue problem
Abstract: S. T. Yau conjectured that the first eigenvalue of every closed minimal
hypersurface in the unit sphere is just its dimension. We prove this conjecture for
minimal isoparametric hypersurfaces. As for the focal submanifolds, which are
minimal submanifolds in the unit sphere, we show that their first eigenvalues are also
equal to their dimensions in the non-stable range. Moreover, we give some estimate on
the other eigenvalues.
8. Xiaolong Han,
California State University, Northridge
Title: Small scale quantum ergodicity on negatively curved manifolds
Abstract: Quantum ergodicity is the study of how the ergodicity (or chaos, i.e. with
exponential instability) of a classical Hamiltonian system is reflected in its
corresponding quantum system. For example, what implication does ergodicity (or
chaos) of the geodesic flow on a compact Riemannian manifold have on the Laplacian
eigenvalues and eigenfunctions? The quantum ergodic theorem states that, if the
geodesic flow is ergodic, then a full density subsequence of the eigenfunctions tend
equidistributed asymptotically. Small scale quantum ergodicity provides stronger and
finer equidistribution than the quantum ergodic theorem. It has been applied to other
estimates of eigenfunctions. I prove that quantum ergodicity up to a small scale holds
on negatively cursed manifolds, using the fact that their geodesic flow display
exponential decay of correlation. I will also talk about the background on dynamical
system, ergodicity, and chaos, in classical and quantum regimes, respectively.
9. Zhiqin Lu,
UC Irvine
Title: on the ground state of quantum layers
Abstract: In this talk, we shall discuss the ground state of a quantum layer. Let
$\Sigma$ be an embedded surface of $R^3$. A quantum layer is the set of points whose
distance to $\Sigma$ is less than a fixed number $a$. We shall see that for many such
quantum layers, the Dirichilet Laplacian has the ground state.
10. Fang Wang,
Title:
Shanghai Jiaotong University
Limit of sharp Sobolev inequalities
Abstract: Consider the sharp Sobolev inequalities on the n-sphere. By assuming the
dimension constant to be a continuous parameter, then the limit of sharp Sobolev
inequalities gives the Moser-Trudinger inequality as n—>2. However, this is a fake
proof of the Moser-Trudinger since the dimension constants can only be integers. In
this talk, I will mainly introduce a new point of view to make the limit to be
mathematically true, by taking advantage of the fractional GJMS operators and their
energy extension to the hyperbolic space.
Participants:
Hua Chen
Wuhan University
Zhigang Chen
Shantou University
Xianzhe Dai
UC Santa Barbara
Qin Ding
Fudan University
Feng Du
Jingchu University of Technology
Huijun Fan
Peking University
Jingwei Guo
University of Science and Technology of China
Xiaolong Han
California State University ,Northridge
Yue He
Nanjing Normal University
Qun He
Tongji University
Xueping Huang
Nanjing University of Information Science & Technology
Jiaxing Hong
Fudan University
Bobo Hua
Fudan University
Yan Huang
Fudan University
Jiacheng Huang
Fudan University
Zhiqin Lu
UC Irvine
Genqian Liu
Beijing Institute of Technology
Shiping Liu
University of Science and Technology of China
Fanghua Lin
Courant Institute for Mathematical Sciences
Xin Luo
Hunan University
Hongquan Li
Fudan University
Jing Mao
Wuhan University of Technology
Shengliang Pan
Tongji University
Ke Shi
Tongji University
Linlin Sun
University of Science and Technology of China
Weixu Su
Fudan University
Fengyu Wang
Beijing Normal University
Kui Wang
Suzhou University
Fang Wang
Shanghai Jiaotong University
Jiayong Wu
Shanghai Maritime University
Meng Wang
Zhejiang University
Hao Wu
Fudan University
Bo Wu
Fudan University
Dongmeng Xi
Shanghai University
Xiaowei Xu
University of Science and Technology of China
Jinju Xu
Shanghai University
Bo Xia
Zhongshan University
Chengjie Yu
Shantou University
Zhenwei Yu
Shantou University
Songting Yin
Tongling University
Wenjiao Yan
Beijing Normal University
Jialin Zhu
Shanghai Center for Mathematical Sciences
Feifei Zhao
Shantou University
Lingzhong Zeng
Jiangxi Normal University
Maomao Zhu
Shanghai Jiaotong University
Yanlong Zhang
Tongji University
Chunqin Zhou
Shanghai Jiaotong University
Jiuru Zhou
Yangzhou University
Hotel:
1.
Hotel: Fudan Yanyuan Hotel
Address： No 270, Zhengtong Road (near Guoding Road), Yangpu
district, Shanghai
Tel：86- 021-65115121
2.
Hotel: Ramada Shanghai Wujiaochang
Address： No 1888 Huangxing Road , Yangpu district, Shanghai
Tel：86- 021-51017070