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

小行星9504176 调查员建议继续他的调查大特征值渐近双曲黎曼曲面。他建议考虑的问题，独特的量子遍历的经典模块组，连接之间的谱渐近和问题的数论，几何的模空间的真实的投影结构的紧凑表面。 黎曼曲面可以被认为是平面的多重覆盖，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（复值函数的图形是四维空间中的曲面）。事实上，它们最初被构造为复值函数的自然域。

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.