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.

我提出的研究将数学的两个领域联系起来：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的枫叶中看到的对称性。 另一方面，数论是数学家给论证起的名字，这些论证最终告诉我们支配整数 1、2、3 等的定律。数论的一个特定领域关注素数，比如 5 这样的数字只需除以 1 和它们本身即可得到整数。 令人惊讶的是，素数有复杂的定律，可以用某种形式的对称性来表达——用群论的语言来表达。 这是我提议的研究领域。 该研究领域主要引起全球数学界的兴趣。 它是人类对数字本身兴趣的延续，并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方面的一些专业知识。