权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Homogeneous Einstein Spaces

齐次爱因斯坦空间

基本信息

批准号：
1906351
负责人：
Michael Jablonski
金额：
$ 31.67万
依托单位：
University of Oklahoma Norman Campus
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2023-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1906351&HistoricalAwards=false
关键词：
Homogeneous Einstein Spaces

项目摘要

This project revolves around the study of natural model spaces. In the past, until a century and a half ago, the only model whose geometry was investigated was (flat) Euclidean space - this is the geometry that we all learned in high school. However, in order to advance science and engineering, we need to use models that incorporate curvature - for example, the Earth is not flat, it is round! To this end, the principal investigator (PI) will study special model geometries called homogeneous Einstein spaces to learn more about their basic properties and work towards their classification. The PI will develop new tools for analyzing these spaces and utilize the graduate student support to train a new generation of mathematicians in their application. The PI will conduct an investigation into homogeneous Einstein metrics by continuing to develop tools from Geometric Invariant Theory and their interaction with tools from Geometric Analysis. The goal of this program is to classify non-compact, homogeneous Einstein manifolds and determine if all such spaces are, in fact, solvmanifolds. Even further, the PI will investigate the distinguished geometric and algebraic properties of Einstein and Ricci soliton spaces.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目围绕自然模型空间的研究。在过去，直到世纪前，唯一的模型，其几何被调查是（平坦的）欧几里德空间-这是我们都在高中学习的几何。然而，为了推进科学和工程，我们需要使用包含曲率的模型-例如，地球不是平的，它是圆的！为此，首席研究员（PI）将研究称为齐次爱因斯坦空间的特殊模型几何，以更多地了解它们的基本性质并致力于它们的分类。 PI将开发新的工具来分析这些空间，并利用研究生的支持来培养新一代的数学家。PI将通过继续开发几何不变理论的工具及其与几何分析工具的相互作用，对齐次爱因斯坦度量进行调查。这个程序的目标是对非紧的齐次爱因斯坦流形进行分类，并确定是否所有这样的空间实际上都是解流形。此外，PI还将研究爱因斯坦和里奇孤子空间的杰出几何和代数性质。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。