2020-06-30 来源：数学科学研究中心

时间：北京时间69日上午9:00-10:00

时间：北京时间62日上午9:00-10:00

ICCM:

5.

The following is the information of the lecture on geometry:

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ID18430443981

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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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ID18430443981

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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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ID18430443981

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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.