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\title{Titles and Abstracts}
\author{http://ims.nju.edu.cn/conference/2010/ }
\date{2010.7.13-15}
\maketitle
{\bf Shu-Cheng Chang} (National Taiwan University)
{\bf Title}: Geometric Evolution Problems in a Closed Pseudohermitian $3$-Manifold
{\bf Abstract}: We consider the CR geometrization problems of contact $3$-manifolds via
the CR curvature flows. An interesting direction is that of finding the CR analogue
of the Ricci flow in a pseudohermitian 3-manifold. In particular, I will discuss
the related topics via the CR Yamabe flow, the Cartan flow as well as the torsion flow.
{\bf Binglong Chen} (Sun Yat-sen University)
{\bf Title}: Complete classification of compact four-manifolds with positive isotropic curvature
{\bf Abstract}: In this talk, I will discuss the complete classification of diffeomorphism types
of all compact four-manifolds with positive isotropic curvature. This in partcular gives
affermative anwers of two conjectures in dimension $4$ due to Gromov and Schoen seperately.
As by-products, we obtain a complete classification of all compact four-manifolds which
are locally conformally flat with positive scalar curvature.
{\bf Yuxin Ge} (University of Paris XII, France)
{\bf Title}: An almost Schur Theorem on 4-dimensional manifolds
{\bf Abstract}: In this talk we show that the almost Schur theorem, introduced by De Lellis-Topping,
is true on 4-dimensional Riemannian manifolds of nonnegative scalar curvature.
This is a joint work with Guofang Wang.
{\bf Qing Han} (Notre Dame, USA)
{\bf Title}: Linearization of isometric embedding and its characteristic variety
{\bf Abstract}: It is an old problem in geometry to study isometric embedding of Riemannian
manifolds in Euclidean space of the Janet dimension. Such an isometric embedding can
be expressed by a first order differential system. The linearization of this system is
highly degenerate. By introducing appropriate parameters, we will reduce this linear
system and discuss its characteristic variety.
{\bf Xiaojun Huang} (Rutgers University, USA)
{\bf Title}: Holomorphic maps between hyperquadrics with small signature
{\bf Abstract}: I will discusss a joint paper with S. Baouendi and P. Ebenfelt on the
classification for holomorphic maps bewteen hyperquadrics with small
signatute.
{\bf Jiayu Li} (ICTP, Italy)
{\bf Title}: Two ways to find holomorphic curves in K\"ahler surfaces
{\bf Abstract}: Let $M$ be a K\"ahler surface and $\Sigma$ be a closed real
surface smoothly immersed in $M$. Let $\alpha$ be the K\"ahler
angle of $\Sigma$ in $M$. If $\cos\alpha>0$, we say $\Sigma$ is a
symplectic surface. We study the problem ``{\it whether there is a
holomorphic curve in the homotopy class of a symplectic surface}".
In the talk we will present two approaches to the problem, one is
the mean curvature flow method, another one is the variational approach.
{\bf Ngaiming Mok} (Hong Kong University) %%(July 12 evening, leave: July 15 morning, °²ÅÅ½Ó»ú)
{\bf Title}: Analytic continuation and rigidity of germs of holomorphic isometries
and measure-preserving maps between bounded symmetric domains
{\bf Abstract:} Motivated by problems in Arithmetic Dynamics in the work of Clozel-Ullmo on Hecke
correspondences, we prove two types of extension and rigidity results concerning germs of holomorphic
maps between bounded symmetric domains. The first type of such results concerns germs of holomorphic
isometries $f: (\Omega,\lambda ds_\Omega^2;0) \to (\Omega', ds_{\Omega'}^2;0)$, where $\Omega$ and
$\Omega'$ stand for bounded symmetric domains and $\Omega$ is irreducible, $ds_\Omega^2$ resp.
$ds_{\Omega'}^2$ stands for the Bergman metric, and $\lambda$ is an arbitrary normalizing constant.
The second type of such results concerns germs of measure-preserving holomorphic maps
$g: (\Omega,\lambda d\mu_\Omega;0) \to (\Omega, d\mu_\Omega;0) \times \cdots \times (\Omega, d\mu_\Omega;0)$
where $\Omega$ is an irreducible bounded symmetric domain, $d\mu_\Omega$ stands for the volume form
of the Bergman metric, and $\lambda$ is again an arbitrary normalizing constant.
{\bf Jie Qing} (UCSC, USA)
{\bf Title}: Spectral characterization of conformally compact Einstein manifolds
with an infinity of positive Yamabe type
{\bf Abstract}: In this talk I will describe a sharp correspondence between the
global geometric properties of a conformally compact Einstein manifold and
the conformal invariants of the infinity. We will introduce the scattering
operators which capture both the global geometric properties of the
bulk space and the conformal structure of the infinity.
{\bf Mei-Chi Shaw} (Notre Dame, USA)
{\bf Title}: The Cauchy-Riemann Equations and $L^2$ Serre Duality On Complex Manifolds
{\bf Abstract}: In this talk we study the closed range property and boundary regularity
of the Cauchy-Riemann equations on domains in complex manifolds. We will discuss
the case for pseudoconcave domains and the null space of the $\bar{\partial}$-Neumann operator.
Recent results for the Cauchy-Riemann equations on product domains and an $L^2$
version of the Serre duality on domains in complex manifolds will be discussed (joint
work with Debraj Chakrabarti).
{\bf Yihu Yang} (Tongji University)
{\bf Title}: A remark on singularities of the period mapping (after Wilfried Schmid)
{\bf Weiping Zhang} (Nankai University) %% (arrive at July 15 afternoon)
{\bf Title}: Generelized Witten genus and vanishing theorems.
{\bf Zhou Zhang} (University of Michigan, USA)
{\bf Title}: Stability of solutions for complex Monge-Ampere equations over closed manifolds
{\bf Abstract}: The question on the stability of solutions comes up naturally after the existence
result. In a joint work with Slawomir Dinew, we generalized Kolodziej's result for the case of
background form being K\"ahler to the degenerate situation. For the same equation, uniqueness is
a straightforward application of stability, but there is also time when the stability result can
be applied without much relation to the uniqueness.
{\bf Xiaohua Zhu} (Peking University) %% (July 12, leave at July 15 or 16)
{\bf Title}: K\"ahler-Ricci flow and deformation of complex structures.
\end{document}