Yau(HSM)Awards
    

 

硕士论文获奖者

注意:所有的获奖者都必须出席2010年的颁奖典礼,颁奖典礼的时间暂定为2010年12月17日。

金奖

姓名: 王賜聖

论文题目: Extensions of multiply twisted pluri-canonical forms

毕业学校: 国立台湾大学

论文摘要: Using Siu’s version of the Ohsawa-Takegoshi theorem and the techniques in proving the invariance of plurigenera developed by Siu and Paun, we show in Theorem 1.1 that for a smooth projective family pluricanonical forms with integrable pseudo-effective twisted coefficients may be lifted from the central fiber to the ambient family.

Our result can be regarded as certain “tensor product version” of the Ohsawa-Takegoshi extension theorem. It unifies and generalizes most of the known extension results for smooth projective families.


银奖(3项,排名不分先后)

在2010年的颁奖典礼上,将授予以下三人银奖,他们将平分奖励标准中提到的两项银奖奖金。

姓名: Yun Kuen Cheung

论文:Analysis of Weighted Digital Sums by Mellin Transform

毕业学校: 香港科技大学

论文摘要: In this thesis, we analyze two types of weighted digital sums (WDS) which arise in algorithm analysis.……

 

姓名: 邓雯

论文题目: Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator and generalizations

毕业学校: Université Pierre et Marie Curie

论文摘要:Motivated by a stability problem in fluid mechanics, we are interested in the spectral and pseudospectral properties of the differential operator $H_\epsilon=-\partial_x^2+x^2+i\epsilon^{-1}f(x)$ on $L^2(\R)$, where $f$ is a real-valued function and $\epsilon>0$ is a small parameter. Under appropriate conditions on $f$, I.Gallagher, T.Gallay and F.Nier gave precise estimates by using localization techniques and semiclassical subelliptic estimates. This master thesis is divided into two parts. Section 1 is a description of the work in the article I.Gallagher, T.Gallay and F.Nier, Section 2 exhibits generalizations to dimension $n$ of the resolvent estimates of the operator $H_\epsilon$ along the imaginary axis.

 

姓名: Fan Sin Tsun

论文题目: Open Orbits and Augmentations of Dynkin Diagrams

毕业学校: 香港中文大学

论文摘要: The study of open orbits in finite dimensional representations has its roots in geometry, representation theory and invariant theory. Our motivation starts from considering the open GLn-orbits in ΛkRn as a local model for defining the stable forms on smooth manifolds. The observation is that such an open GLn –orbit exists in ΛkRn exactly when the Dynkin diagram of slnC, i.e. of type An-1, can be extended to another Dynkin diagram by attaching an extra node to the k-th node of the original diagram. In this thesis, we will fully elaborate this idea using techniques in representation theory. We show that an augmentation of Dynkin diagrams provides a structure of Z-gradation on the ambient Lie algebra corresponding to the larger Dynkin diagram and the 0-th graded piece is then a reductive Lie subalgebra whose semisimple part is associated to the smaller Dynkin diagram. Passing to the group level, we obtain an irreducible representation which admits a finite number of orbits, which will be called an irreducible prehomogeneous vector space of parabolic type. We also consider other cases of irreducible representations which admit an open orbit but not coming from an augmentation of Dynkin diagrams. Finally, we mention a generalization of prehomoegeneous vector spaces of parabolic type to the visible representations motivated from invariant theory and a treatment of the real forms of irreducible prehomogeneous vector spaces of parabolic type.

 

 

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