Mathematical Sciences: Spectral Asymptotics for Hyperbolic Surfaces and Real-Projective Structures

9504176 Wolpert研究者建议继续他对双曲黎曼曲面的大特征值渐近性的研究。他建议考虑经典模群的唯一量子遍历性问题，谱渐近与数论问题之间的联系，紧曲面实射影结构的模空间几何。黎曼曲面可以被认为是平面的多层覆盖；具有有趣的拓扑性质。此外，黎曼曲面在复值函数的研究中起着至关重要的作用（复值函数的图是四维空间中的曲面）。事实上，它们最初是作为复值函数的自然域构造的。

9504176 Wolpert The investigator proposes to continue his investigations of the large eigenvalue asymptotics of hyperbolic Riemann surfaces. He proposes to consider the question of unique quantum ergodicity for the classical modular group, connections between spectral asymptotics and questions in number theory, and the geometry of the moduli space of real projective structures for a compact surface. Riemann surfaces can be thought of as multi-sheeted covers of the plane; have interesting topological properties. In addition, Riemann surfaces play a crucial role in the study of complex-valued functions (the graph of a complex-valued function is a surface in a 4-dimensional space). Indeed they were originally constructed as natural domains for complex-valued functions.