Real groups, Hodge theory, and the Langlands program

实群、霍奇理论和朗兰兹纲领

• 批准号: DP180101445
• 负责人: Prof Kari Vilonen
• 金额: $ 19.09万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-25 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180101445
• 关键词: Real; groups; Hodge; theory; Langlands

This mathematics project aims to settle open questions in real groups. The real groups are the fundamental symmetries occurring in nature and are important both in number theory and in the physical sciences. In particular, this project aims to reach a comprehensive understanding of Langlands duality for real groups, investigate how Hodge theory can be used to describe the unitary dual, and investigate the micro-local structure of systems of differential equations. Potential benefits include increasing the international stature of mathematics in Australia and improving the quality of the workforce.

这个数学项目旨在解决真实的群体中的开放性问题。真实的群是自然界中最基本的对称性，在数论和物理科学中都很重要。特别是，这个项目的目的是达到一个全面的了解朗兰兹对偶的真实的群体，研究如何霍奇理论可以用来描述酉对偶，并研究微分方程系统的微观局部结构。潜在的好处包括提高澳大利亚数学的国际地位和提高劳动力的质量。