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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759243
• 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.

我提出的研究在数学的两个领域建立了联系：群体理论和数理论。 在数学语言中，组是一个编码对称性的对象。 例如，有一个特定的组描述了我们在加拿大旗上的枫叶中看到的对称性。 另一方面，数字理论是数学家给出的名称，最终告诉我们有关总数1,2,3等法律的论点。仅除以1，然后将其提供全数字。 令人惊讶的是，有一些复杂的质数定律可以表达为某种形式的对称性 - 用群体理论的语言表示。 这是我建议的研究领域。该研究领域主要对全球数学社区感兴趣。 这是为了自己的缘故，人类对数字的兴趣的延续，并揭示了他们神秘的结构。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。