GRK 1269: Global Structures in Geometry and Analysis

GRK 1269：几何和分析中的全局结构

• 批准号: 968940
• 金额: --
• 依托单位: Universität zu Köln
• 依托单位国家: 德国
• 项目类别: Research Training Groups
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/968940?language=en
• 关键词: GRK; 1269; Global; Structures; Geometry

Manifolds are geometric spaces, which are described by systems of non-linear equations. They appear in almost all fields of mathematics and its applications, e.g. as phase or model spaces in physics and applied mathematics, as minimal surfaces and spaces with certain curvature properties in differential geometry, or as modular varieties in number theory. The manifolds encountered in practice will always carry an additional global structure that encodes information about the context in which they were defined. For instance, the phase spaces of mechanics or optics carry a symplectic or a contact structure, twistor spaces over certain Riemannian manifolds are complex and uniruled.

流形是由非线性方程组描述的几何空间。它们几乎出现在数学及其应用的所有领域，如物理学和应用数学中的相空间或模型空间，微分几何中的极小曲面和具有某些曲率性质的空间，或数论中的模变异体。在实践中遇到的流形将始终携带一个附加的全局结构，该结构编码关于它们被定义的上下文的信息。例如，力学或光学的相空间具有辛结构或接触结构，某些黎曼流形上的扭转空间是复杂的和不规则的。

项目成果

The fractional Cheeger problem

• DOI: 10.4171/ifb/325
• 发表时间: 2013-08
• 期刊: arXiv: Analysis of PDEs
• 作者: L. Brasco;E. Lindgren;E. Parini

Special values of shifted convolution Dirichlet series

移位卷积狄利克雷级数的特殊值

• DOI: 10.1112/s0025579315000169
• 发表时间: 2015
• 期刊: arXiv: Number Theory
• 作者: M.H. Mertens;K. Ono
• 通讯作者: K. Ono

Asymptotic formulae for partition ranks

• DOI: 10.4064/aa168-1-5
• 发表时间: 2014-06
• 期刊: arXiv: Number Theory
• 作者: Jehanne Dousse;Michael H. Mertens

Morse–Bott inequalities in the presence of a compact Lie group action and applications

存在紧李群作用时的 MorseâBott 不等式及应用

• DOI: 10.1016/j.difgeo.2013.11.003
• 发表时间: 2014
• 期刊: Differential Geometry and Its Applications
• 影响因子: 0.5
• 作者: Wen Lu

Congruences for the Fourier coefficients of the Mathieu mock theta function

Mathieu 模拟 theta 函数的傅里叶系数的同余式

• DOI: 10.1016/j.jnt.2014.09.025
• 发表时间: 2015
• 期刊: Journal of Number Theory
• 影响因子: 0.7
• 作者: T. Miezaki;M. Waldherr
• 通讯作者: M. Waldherr