已开展的网上讨论班信息(截至7.7)

2020-06-30 来源:数学科学研究中心

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活动类型:学术报告

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活动时间:2020-06-30 12:37:05--2020-06-30 12:37:05

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已开展的网上讨论班信息(截至7.7

 

浙江大学数学中心:

 

第六周论文讨论班

时间:北京时间77日上午9:00-10:00

地点:腾讯会议(会议号:212 989 785 无密码)

报告人:刘凯

题目:Holomorphic mappings into non-negatively curved manifolds

摘要:In this talk, we first recall Stepanov and Tsyganoks’ results on harmonic mappings into non-negatively curved Riemannian manifolds and holomorphic mappings into non-negatively curved Complex manifolds. Then we generalize their results under a weak curvature condition(the non-negative quadratic orthogonal bisectional curvature, NNQOBC for short). Also, considering the identity mapping of a compact Kähler manifold with two different Ka ̈hler metrics, we obtain a uniqueness theorem for Ricci tensor. At last, we consider the harmonic mapping from P^1 to a Kähler manifold with NNQOBC and obtain a rigidity theorem.

 

第五周论文讨论班

时间:北京时间6.30上午9:00-10:00

地点:腾讯会议(会议号:532 136 222 无密码)

报告人:李逸

题目:The square of Nijenhuis tensor and applications, (Jun Ling, arXiv: 2005.08647)

摘要:报告下Ling Jun 最近关于球面上近复结构和复结构的文章。

 

第四周论文讨论班

时间:北京时间623日上午9:00-10:00

地点:腾讯会议(会议号:370 928 751 无密码)

报告人:张良迪

题目:Harnack estimates for a nonlinear diffusion equation on compact Kähler manifolds

摘要:In this talk, we survey the progress of Harnack estimates on manifolds, and prove some Harnack estimates for a positive solution to the equation $\partial_tu=\Delta u+au+bu^{p+1}$ on a compact Kähler manifold.

 

第三周论文讨论班(第二场)

时间:北京时间618日上午9:00-10:00

地点:腾讯会议(会议号:303 986 232 无密码)

报告人:夏天澄

题目:Little notes on the degeneration of Balanced cone and Gauduchon cone.

摘要:We give some basic notes of  three cohomology group and its common cone (Balanced cone & Gauduchon cone)  on the compact complex manifold . Then we discuss the condition that the Gauduchon cone degenerates but Balanced cone does not , using the ddbar-lemma and the isomorphism map between Bott-Chern cohomology group and Aeppli cohomology group, and give the distance of Bx from degeneration.

 

第三周论文讨论班(第一场)

时间:北京时间616日上午9:00-10:00

地点:腾讯会议(会议号:807 800 809 无密码)

报告人:陈如通

题目:Algebraic deformations of compact Kähler surfaces

摘要:Kodaira has proved that every compact Kähler surface is a deformation of an algebraic surface. Buchdahl's paper Algebraic deformations of compact Kähler surfacesgives a short proof of it under the extra assumption that all infinitesimal deformations are unobstructed. My talk is going to introduce the main theorem of Buchdahl's paper.

 

第二周论文讨论班

 时间:北京时间69日上午9:00-10:00

地点:腾讯会议(会议号:614 381 906 无密码)

报告人:纪正超

题目:Ancient solutions of codimension two surfaces with curvature pinching in R^4

摘要:We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [28] and we also remove the condition that the second fundamental form is uniformly bounded when t (−,−1).

 

第一周论文讨论班

 时间:北京时间62日上午9:00-10:00

地点:腾讯会议(会议号:903 691 934 无密码)

报告人:张良迪

题目:On gradient shrinking and expanding Kähler-Ricci solitons

摘要:In this talk, we prove a compact gradient shrinking Kähler-Ricci soliton with subharmonic scalar curvature is Kähler-Einstein. Moreover, we show that a complete noncompact gradient shrinking Kähler-Ricci soliton with harmonic scalar curvature and nonnegative fourth order divergence curvature (or Bochner) tensor is rigid. We also prove that a classification theorem for complete noncompact gradient expanding Kähler-Ricci solitons.

 

 

 

ICCM:

5.

The following is the information of the lecture on geometry:

 

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ICCM Lectures on Geometry

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Title: A characterization of non-compact ball quotient

 

Speaker: Prof. Ya Deng (IHES)

Time: 3pm -4pm (Friday, 2020-07-03)

Abstract: In 1988 Simpson extended the Donaldson-Uhlenbeck-Yau theorem to the context of Higgs bundles, and as an application he proved a uniformization theorem which characterizes complex projective manifolds and quasi-projective curves whose universal coverings are complex unit balls. In this talk I will give a characterization for quasi-projective manifolds to be uniformized by complex unit balls, which generalizes the uniformization theorem by Simpson. 

 

4.

The following is the information of the lecture on geometry:

 

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ICCM Lectures on Geometry

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Title: Localization of eta invariant

Speaker: Prof. Bo Liu (East China Normal University)

Time: 10:00 am -11:00 am (Friday, 2020-06-26)

Abstract: The famous Atiyah-Singer index theorem announced in 1963 computed the index of the elliptic operator, which is defined analytically, in a topological way. In 1968, Atiyah and Segal established a localization formula for the equivariant index which computes the equivariant index via the contribution of the fixed point sets of the group action. It is natural to ask if the localization property holds for the more complex spectral invariants, e.g., eta-invariant.

The eta-invariant was introduced in the 1970's as the boundary contribution of index theorem for compact manifolds with boundary. It is formally equal to the number of positive eigenvalues of the Dirac operator minus the number of its negative eigenvalues and has many applications in geometry, topology, number theory and theoretical physics. It is not computable in a local way and not a topological invariant. In this talk, we will establish a version of localization formula for equivariant eta invariants by using differential K-theory, a new research field in this century. This is a joint work with Xiaonan Ma.

 

3.

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ICCM Lectures on Geometry

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Title: On a canonical bundle formula with $\R$-coefficients

Speaker: Zhengyu Hu (Chongqing University of Technology)

Time: 10:00 am -11:00 am (Friday, 2020-06-19)

Abstract: In this talk, I will discuss a canonical bundle formula for a proper surjective morphism 

(not necessarily with connected fibers) with  $\R$-coefficients and its applications. Moreover, I will discuss the inductive property of the moduli divisor.

 

2.

The ICCM lecture on Geometry is rescheduled this week. It is at 10:00 am -11:00 am (Saturday, 2020-06-13). 

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ICCM Lectures on Geometry

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Title: Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Speaker: Wenhao Ou (AMSS)

Time: 10:00 am -11:00 am (Saturday, 2020-06-13)

Abstract: In this talk we will discuss the structure of projective manifold $X$ whose tangent bundle contains a locally free strictly nef subsheaf. We establish that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group $\pi_1(X)$ is virtually abelian, then $X$ is isomorphic to a projective space. This is joint work with Jie Liu (MCM) and Xiaokui Yang (YMSC).

 

1.

ICCM Lectures on Geometry

 

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Title: Complex structures on Einstein four-manifolds of positive scalar curvature

Speaker: Peng Wu (Fudan University)

Time: 10:00 am -11:00 am (Friday, 2020-06-05)

Abstract: In this talk we will discuss the relationship between complex structures and Einstein metrics of positive scalar curvature on four-dimensional Riemannian manifolds. One direction, that is, when a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. We will consider the other direction, that is, when a four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.

Our method relies on Derdzinski's proof of the Weitzenbock formula for the self-dual Weyl curvature.