New approaches to index theory

指数理论的新方法

• 批准号: DP0770927
• 负责人: Prof Mathai Varghese
• 金额: $ 33.71万
• 依托单位: The University of Adelaide
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2007
• 资助国家: 澳大利亚
• 起止时间: 2007-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0770927
• 关键词: New; approaches; index; theory

The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.

自然定律通常用微分方程来表达，包括它们的变化率。如果是“椭圆型”，则它们有一个“指数”，即解的数量减去所施加的约束的数量。Atiyah-Singer指数定理给出了这个“指数”的惊人计算。分数阶指数理论是一个扩展，它解决了一个基本的开放问题，受到国际关注。一个中心目标是进一步调查这一点。我将帮助初学者通过研讨会，春季学校和监督导航到研究的前沿。其好处包括提高澳大利亚在国际研究前沿的地位。