Twisted endoscopy from the sheaf-theoretic perspective

从束理论角度看扭曲内窥镜

• 批准号: RGPIN-2017-06361
• 负责人: Mezo, Paul
• 金额: $ 1.17万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711988
• 关键词: Twisted; endoscopy; sheaf; theoretic; perspective

My proposed research makes connections in two areas of mathematics: group theory, and number theory. In mathematical language a group is an object that encodes symmetry. For instance there is a specific group describing the symmetry we see in the maple leaf on the Canadian flag. On the other hand, number theory is the name mathematicians give to arguments that ultimately tell us about the laws governing the whole numbers 1,2,3, etc. A particular area of number theory is focused on prime numbers, numbers like 5 which can only be divided by 1 and themselves to give whole numbers. Surprisingly, there are complicated laws of prime numbers which can be expressed as some form of symmetry--that is expressed in the language of group theory. This is my proposed area of research. This area of research is of interest mainly to the global mathematical community. It is a continuation of humanity's interest in numbers for their own sake, and reveals their mysterious structure. My research represents some of Canada's expertise in this venerable and vigorous tradition.

我提出的研究在两个数学领域建立了联系：群论和数论。在数学语言中，群是编码对称性的对象。例如，有一个特定的组描述了我们在加拿大国旗上看到的枫叶的对称性。另一方面，数论是数学家给论点起的名字，这些论点最终告诉我们支配整数1、2、3等的规律。数论的一个特定领域专注于素数，像5这样的数字只能被1整除，然后它们自己才能得出整数。令人惊讶的是，有复杂的素数定律可以用某种形式的对称性来表示--这是用群论的语言来表示的。这是我建议的研究领域。 这一研究领域主要是全球数学界感兴趣的。它延续了人类对数字本身的兴趣，揭示了数字的神秘结构。我的研究代表了加拿大在这一古老而充满活力的传统中的一些专业知识。