Kaehler manifolds, automorphic forms, and quantization

凯勒流形、自守形式和量子化

• 批准号: 311866-2011
• 负责人: Barron, Tatyana
• 金额: $ 0.8万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508434
• 关键词: Kaehler; manifolds; automorphic; forms; quantization

I work on questions in analysis and geometry that have strong connections to the classical theory of automorphic forms (where the foundational work was done by Baily, Borel, Harish-Chandra, Piatetski-Shapiro, and others), and, on the other hand, to geometric quantization, which is an area of symplectic geometry whose development was pioneered by Kirillov, Kostant, Souriau and others. My earlier work provided information about asymptotic behaviour of sections of line bundles, about curvature of certain connections in vector bundles, about Toeplitz operators, and also explicit description of spaces of automorphic forms, often associated to some geometric data.

我工作的问题在分析和几何有很强的联系，以古典理论的自守形式（其中的基础工作是由Beveli，博雷尔，哈里什-钱德拉，皮亚特斯基-夏皮罗，和其他人），并在另一方面，几何量化，这是一个领域的辛几何的发展是开创性的基里洛夫，科斯坦特，苏里奥和其他人。我早期的工作提供了有关渐近行为的部分线丛，曲率的某些连接在向量丛，关于Toeplitz运营商，并明确描述空间的自守形式，往往与一些几何数据。