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Geometry from Donaldson-Thomas invariants

唐纳森-托马斯不变量的几何

基本信息

批准号：
EP/V010719/1
负责人：
Thomas Bridgeland
金额：
$ 78.42万
依托单位：
University of Sheffield
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FV010719%2F1
关键词：
Geometry Donaldson Thomas invariants

项目摘要

There has long been a close relationship between pure mathematics and theoretical physics. Many subfields of mathematics began with attempts to address problems from theoretical physics. A famous example is Newton's development of calculus, which he applied to understand the motion of the planets. On the other hand mathematics provides an essential language for physicists to describe their theories, and calculations tools for them to make precise predictions.In the last few decades this relationship between maths and physics has become extremely deep and important. The present-day interaction revolves around a subject called quantum field theory, which is an incredibly powerful calculational tool in theoretical physics, but which has not yet been understood in precise mathematical terms. Quantum field theory has been described as being the calculus of infinite dimensions.This proposal is about a class of problems in pure mathematics which are closely related to important ideas in quantum field theory. Our aim is to understand the solutions to these problems in particular cases, and to prove a general result which shows that they can always be solved. Collaborating with theoretical physicists, and trying to reformulate their ideas in mathematical terms is an important part of this work. As well as leading to new and interesting mathematics, our hope is that this research will lead to new insights in quantum field theory.

纯数学与理论物理之间的关系由来已久。数学的许多子领域都是从解决理论物理问题的尝试开始的。一个著名的例子是牛顿对微积分的发展，他用微积分来理解行星的运动。另一方面，数学为物理学家描述他们的理论提供了必要的语言，为他们做出精确的预测提供了计算工具。在过去的几十年里，数学和物理之间的这种关系变得极其深刻和重要。目前的相互作用围绕着一门名为量子场论的学科展开，这是理论物理中一种极其强大的计算工具，但人们还没有用精确的数学术语来理解它。量子场论一直被描述为无限维微积分。这一提议是关于一类与量子场论中的重要思想密切相关的纯数学问题。我们的目标是了解这些问题在特定情况下的解决方案，并证明一个表明这些问题总是可以解决的一般结果。与理论物理学家合作，并试图用数学术语重新表述他们的想法是这项工作的重要组成部分。除了导致新的和有趣的数学，我们希望这项研究将导致对量子场论的新见解。