Mathematical Sciences: Complex Manifold Theory and Kaehler Geometry

DMS-9500999 Siu 萧将研究复流形理论和Kaehler几何中的几个相关问题。 这些问题包括双曲性问题，有效自由和非常丰富，一般Bochner型公式和几何超刚性，以及紧致埃尔米特对称流形的整体不可变形性。 多复变出现在世纪初作为一个自然的产物研究的职能，一个复杂的变量。 很明显，这个理论与它的前身有很大的不同。 基本的几何是更难以把握和函数理论有更多的亲和力与偏微分算子的一阶。 因此，它成长为一个混合学科结合了微分几何和微分方程的深刻特点。 许多基本结构是在过去三十年中确定的。 目前的研究仍然集中在理解这些基本的数学形式。

DMS-9500999 Siu Siu will investigate several related problems in complex manifold theory and Kaehler geometry. These include hyperbolicity problems, effective freeness and very ampleness, general Bochner type formula and geometric superrigidity, and global nondeformability of compact hermitian symmetric manifolds. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.