GRK 1133: Geometry and Analysis for Symmetries

GRK 1133：几何和对称性分析

• 批准号: 776961
• 金额: --
• 依托单位: Universität Paderborn
• 依托单位国家: 德国
• 项目类别: International Research Training Groups
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/776961?language=en
• 关键词: GRK; 1133; Geometry; Analysis; Symmetries

The analysis of systems with symmetries involves a number of different mathematical fields from representation theory and harmonic analysis, the theory of integral transformations, symplectic/complex and non-commutative geometry as well as infinite dimensional differential geometry and quantisation. Even though many central questions in the analysis of symmetries are still open, their study has produced a wealth of deep results with very diverse applications to fields such as partial differential equations, mathematical physics, number theory, ergodic theory, complex analysis, and index theory.

系统的对称性分析涉及到许多不同的数学领域，从表示论和调和分析，积分变换理论，辛/复和非交换几何以及无穷维微分几何和量子化。尽管对称性分析中的许多中心问题仍然是开放的，但他们的研究已经产生了大量深刻的结果，并在偏微分方程、数学物理、数论、遍历理论、复分析和指数理论等领域有着非常广泛的应用。