Twisted endoscopy from the sheaf-theoretic perspective

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，群是一个编码对称的对象。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，数论是数学家给那些最终告诉我们支配整数1、2、3等的定律的论证起的名字。数论的一个特定领域专注于质数，像5这样的数字只能被1整除，然后它们自己得到整数。令人惊讶的是，素数的复杂规律可以用某种形式的对称性来表达——用群论的语言来表达。这是我打算研究的领域。这一研究领域主要是全球数学界感兴趣的。这是人类对数字本身兴趣的延续，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。

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.