Mathematical Sciences: Differential Geometry and Riemann Surfaces

两名高级研究员和两名博士后将研究微分几何和黎曼曲面的各个方面。我们将建立弦理论对所有阶微扰理论的有限性。这将需要发展全纯超几何和Feynman图所建议的TeichMuller空间的新的参数化。第二位研究员将研究复杂微分几何中的问题。这将包括对厄米对称域、它们之间的全纯映射以及它们的分类的研究。一名博士后将分析紧致复双曲空间形式之间的同态浸入。第二部分将进一步得到具有锥形奇点的流形的特征值的估计。四名研究人员将研究微分几何的各个方面。要研究的几个问题都起源于弦理论。这一理论被用来描述基本粒子之间的复杂相互作用。在这个理论中，每个粒子由一根在十维空间中振动的弦来表示。这些研究是数学家和物理学家不断努力的一部分，目的是使用这一新理论来解释高能粒子实验的结果。

Two senior investigators and two postdocs will study various aspects of differential geometry and Riemann surfaces. One will establish the finiteness of string theories to all orders of perturbation theory. This will require the development of holomorphic supergeometry and new parametrizations of Teichmuller space suggested by Feynman diagrams. The second investigator will work on problems in complex differential geometry. This will include a study of Hermitian symmetric domains, holomorphic mappings between them, and their classification. One postdoc will analyze homomorphic immersions between compact complex hyperbolic space forms. The second will derive further estimates for eigenvalues of manifolds with conelike singularities. Four investigators will study various aspects of differential geometry. Several of the problems to be studied have their origins in string theory. This theory has been used to describe complex interactions between elementary particles. In this theory, each particle is represented by a string which vibrates in ten dimensional space. These investigations are part of a continuing effort by mathematicians and physicists to use this new theory to explain the results of high-energy particle experiments.