Advances in Index Theory

指数理论的进展

• 批准号: DP130103924
• 负责人: Prof Mathai Varghese
• 金额: $ 46.3万
• 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: 2013
• 资助国家: 澳大利亚
• 起止时间: 2013-06-30 至 2016-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP130103924
• 关键词: Advances; Index; Theory

The laws of nature are often expressed in terms of differential equations which, if 'elliptic', have an 'index' being the number of solutions minus the number of constraints imposed. The Atiyah-Singer Index Theorem gives a striking calculation of this 'index', and this project involves innovative extensions of this theory with novel applications.

自然定律通常用微分方程来表示，如果是“椭圆”，则有一个“指数”，即解的数量减去所施加的约束的数量。阿蒂亚-辛格指数定理给出了该“指数”的惊人计算，该项目涉及该理论的创新扩展和新颖的应用。