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.

我研究了与自动形式的经典理论有密切联系的分析和几何形状问题（其中基础工作是由Baily，Borel，Harish-Chandra，Piatetski-Shapiro等人完成的），另一方面，对于几何量化而言，这是几何量化的几何量化，这是kirirov sirov and kirirov sirov and kirirov and kirirov and kirirov。我的早期工作提供了有关线束束的渐近行为的信息，涉及向量束中某些连接的曲率，关于toeplitz operators的曲率，以及对自动形式的空间的明确描述，通常与某些几何数据有关。