Equidistribution, Invariant Measures and Applications

该奖项为将于2019年5月19日至5月24日在耶路撒冷希伯来大学举行的题为“均匀分布、不变措施和应用”的会议提供参与者支持。由幂等元生成的群的作用理论，也被称为Ratner理论，是现代遍历理论的基石。会议的目标是审查该领域的最新发展，并确定新的方向。会议的主要议题将是：幂等流及其在计数和均匀分布中的应用；齐次空间上的对角流及其在算术和其他方面的应用；阿贝尔和二次微分的模空间上的动力学的测度和轨道分类结果；齐次和非齐次空间中的平稳测度和相关的随机游动。会议结构将包括迷你课程、讲座和讨论和协作时间。有关此次会议的更多详细信息，请访问http://ias.huji.ac.il/22midrashamathematicae。这一奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.