| 时 间 | 地 点 | 报告人 | 题目与摘要 |
|---|---|---|---|
| 2017年3月1日 14:00-15:00 | 蒙民伟楼1105室 | 王宏玉(扬州大学) | A note on the deformations of almost complex structures on closed four manifolds |
| 2017年3月8日 16:00-17:00 | 蒙民伟楼1105室 | 李皓昭(中国科学技术大学) |
In this talk, I will show that the mean curvature blows up at the first
finite singular time for a closed smooth embedded mean curvature flow in
R^3. This is joint work with Bing Wang.
|
| 2017年3月16日(周四) 10:00-11:00 | 蒙民伟楼1105室 | 李宇翔（清华大学） |
We will generalize Helein's convergence theorem and give some applications.
|
| 2017年3月22日 | 蒙民伟楼1105室 | 无 | 无 |
| 2017年3月29日 15:00-16:00 | 蒙民伟楼1105室 | 韩青（University of Notre Dame and BICMR） |
A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant
scalar curvatures. In this talk, we study whether these metrics have negative Ricci curvatures. The polyhomogeneous
expansions for solutions of the Yamabe equation play an important role in the study.
|
| 2017年4月5日 14:00-15:00 | 蒙民伟楼1105室 | 王作勤（中国科学技术大学） |
It is well known that the spectrum of the Laplace-Beltrami operator is quite rigid
with respect to the metric. People suspect that on any compact manifold, the set
of Riemannian metrics that are isospectral to any given metric is compact with respect
to the $C^\infty$ topology. For surfaces this has been proven by Osgood-Phillips-Sarnark.
For 3-manifolds Chang-Yang proved the isospectral compactness in any conformal class.
For 4-manifolds the only known results are the ones due to Xu and Chen-Xu: they proved
the isospectral compactness in conformal class for 4-manifolds under certain conditions.
Following Chang-Yang and Chen-Xu, we will give another set of conditions under which the
isospectral compactness in conformal class can be proved. This is a joint work with Xianfu Liu.
|
| 2017年4月12日 15:00-16:00 | 蒙民伟楼1105室 | 熊金刚（北京师范大学） |
In the talk, I will show that optimal constants of fractional Sobolev inequalities depend on
the domains, and can be achieved in many cases, which is different from the classical Sobolev
inequalities in domains. This is joint work with Rupert L. Frank and Tianling Jin.
|
| 2017年4月19日 | 蒙民伟楼1105室 | 无报告 | 无报告 |
| 2017年4月26日 15:00-16:00 | 蒙民伟楼1105室 | 吕鹏 （University of Oregon） |
Ancient solutions of Ricci flow arise naturally when finite time singular solutions of the flow are blown up. We generalize the circle
bundle examples of ancient solutions discovered by Bakas, Kong and Ni to a class of principal torus bundles over an arbitrary finite
product of Fano Kahler-Einstein manifolds studied by Wang and Ziller in the context of Einstein geometry. As a result, continuous families of
kappa-collapsed and kappa-noncollapsed ancient solutions of type I are obtained on circle bundles for all odd dimensions greater than or equal
to 7.
|
| 2017年5月3日 14:00-15:00 | 蒙民伟楼1105室 | 华波波 （复旦大学） |
用边长为1的正多边形作为砖块，将平面拓扑意义下铺满。对于每个顶点处的顶角和不超过360度的铺砖方式，有什么样的组合和几何限制？如何实现？
|
| 2017年5月10日 14:00-15:00 | 蒙民伟楼1105室 | 张影（苏州大学） |
Atiyah proposed his independence conjecture in about 2000 aiming at a solution to a problem in physics.
Given n distinct points in a Euclidean space, a set of n − 1 unit vectors is naturally associated to
each of the given points, and, regarding each unit vector as a complex number via the stereographic
projection, one obtains a monic polynomial of degree n − 1 having as roots the n − 1 complex numbers
corresponding to the unit vectors. The conjecture asserts that the set of n polynomials so obtained
is linearly independent over C. There is a similar conjecture for points in a hyperbolic space. The
conjecture has been proved for the case of four points in a Euclidean space, and the case of four points
in a hyperbolic space which do not lie in a hyperbolic plane. In joint work with Jiming Ma, we confirm
Atiyah’s linear independence conjecture for the case of four points in a hyperbolic plane.
|
| 2017年5月11日 (周四) 9:30-10:30 | 蒙民伟楼1105室 | 来米加（上海交通大学） |
A classical theorem in differential geometry asserts that embedded hypersurfaces with constant H_k
curvature must be spheres, where $H_k$ stands for the $k$-th order mean curvature. In this talk,
I shall present some generalization of this result. More precisely, we show that any convex embedded
hypersurface with point singularities and constant $H_k$ curvature must be a sphere, for $1\leq k< n$.
For k=n, there do exist singular convex hypersurface with constant Gaussian curvature on its smooth part,
but if there are only two singular points, then it must be a football. This is a joint work with Hao Fang
and Weifeng Wo.
|
| 2017年5月17日 16:00-17:00 | 蒙民伟楼1105室 | 杨翎 （复旦大学） |
Lawson-Osserman constructed three types of non-parametric minimal cones of higher codimension based on
Hopf fibrations between Euclidean spheres, which can been seen as Lipschitz solutions to the minimal
surface equations which are not differentiable, thereby making sharp contrast to the regularity theorem
for minimal hypersurfaces in Euclidean spaces. In this paper, the above constructions are generalized
in a more general scheme. Once a mapping f can be written as the composition of a Riemannian submersion
from a Euclidean sphere and an isometric minimal immersion into another Euclidean sphere, the graph of
f yields a non-parametric minimal cone. Because the choices of the second component form huge moduli
spaces, our constructions produce a constellation of uncountable many examples. For each such cone, there
exists an entire minimal graph whose tangent cone at infinity is just the given one. Moreover, surprising
phenomena on the existence, non-uniqueness and non-minimizing for the Dirichlet problem are discovered,
due to the amusing spiral asymptotic behaviour of a particular autonomous system on the 2-plane.
|
| 2017年5月18日 (周四) 10:00-11:00 | 蒙民伟楼1105室 | 莫小欢 （北京大学） |
In this lecture，we discuss some basic theory of Finsler metrics. We determine the flag curvature of
Finsler metric produced from any Finsler metric and any conformal field in terms of the navigation
problem and therefore we provide a unifying frame work for the fundamental equations due to Bao-Robles-Shen,
Cheng-Shen, Foulon and Mo-Huang.
|
| 2017年5月24日 | 蒙民伟楼1105室 | 无报告 | 无报告 |
| 2017年5月31日 | 蒙民伟楼1105室 | 无报告 | 无报告 |
| 2017年6月8日（周四）10:00-11:00 | 蒙民伟楼1105室 | 张会春 （中山大学） |
One of most fundamental theorems in spectral geometry is the Weyl’s law: on any closed n-dimensional
Riemannian manifold, we have a leading asymptotic for eigenvalues of Laplace operator. In this talk,
we will introduce an extension of the Weyl’s law to metric measure spaces with generalized Ricci
curvature bounded from below. This is a joint work with Prof. Xi-Ping Zhu.
|
| 2017年6月14日 15:00-16:00 | 蒙民伟楼1105室 | 关波 （Ohio State University） |
Subsolutions play very important roles in the study of fully nonlinear equations. In this talk we shall
discuss different notions of subsolutions and how they can be used to deriving priori estimates for equations
on closed manifolds. We shall also show the equivalence between some of the definitions of Type I cones
(defined by Caffarelli, Nirenberg and Spruck). In the second part of the talk we shall discuss some
preliminary results on gradient estimates for equations on Riemannian manifolds.
|
| 2017年6月21日 15:00-16:00 | 蒙民伟楼1105室 | 邱春晖（厦门大学） |
In this paper, by using dd-bar-Bochner-Kodaira technique obtained by Y.T.Siu, we get some vanishing theorems on
strictly pseudoconvex complex Finsler holomorphic vector bundles. Moreover, we obtain the Hodge theorems on
strictly pseudoconvex complex Finsler holomorphic vector bundles. In particular, on strictly pseudoconvex
complex Berwald holomorphic vector bundles, we can get the Hodge isomorphism theorems and vanishing theorems
for cohomology groups. This work is joint with Jinling Li and Tongde Zhong.
|
| 2017年6月28日 | 蒙民伟楼1105室 | TBA | TBA |