Equidistribution, Invariant Measures and Applications

均衡分布、不变测度及其应用

• 批准号: 1930145
• 负责人: Dmitry Dolgopyat
• 金额: $ 2.1万
• 依托单位: University of Maryland, College Park
• 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: 2019-05-01 至 2020-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1930145&HistoricalAwards=false
• 关键词: Equidistribution; Invariant; Measures; Applications

This award provides participant support to a conference titled "Equidistribution, Invariant Measures and Applications", to be held on May 19 - May 24, 2019 at the Hebrew University of Jerusalem. The theory of actions of groups generated by unipotent elements also known as Ratner theory is a cornerstone of modern ergodic theory. The goal of the conference is to review the recent developments in the field and to set up new directions. The main topics of the conference will be unipotent flows and their applications to counting and equidistribution; diagonal flows on homogenous spaces, and their applications in arithmetic and beyond; measure and orbit classification results for dynamics on moduli spaces of abelian and quadratic differentials; stationary measures and associated random walks in the homogeneous and non-homogeneous spaces. The conference structure will include mini-courses, lectures, and times for discussion and collaboration. More details about the conference could be found at http://ias.huji.ac.il/22midrashamathematicae .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.

该奖项提供参与者支持题为“等分布，不变的措施和应用”，将于2019年5月19日至5月24日在耶路撒冷希伯来大学举行的会议。由单幂元生成的群的作用理论也被称为拉特纳理论，是现代遍历理论的基石。会议的目的是回顾该领域的最新发展，并确定新的方向。会议的主要议题将是单幂流及其应用计数和equidistribution;对角流的同质空间，及其应用在算术和超越;措施和轨道分类结果的动态模空间的阿贝尔和二次微分;固定措施和相关的随机游动在均匀和非均匀空间。会议结构将包括小型课程，讲座，以及讨论和合作的时间。关于会议的更多细节可以在http://ias.huji.ac.il/22midrashamathematicae上找到。这个奖项反映了NSF的法定使命，并被认为值得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来支持。