Lie Groups: Dynamics, Rigidity, Arithmetic

AbstractLubotzky该奖项提供部分支持为期四天的国际会议，以涵盖最近的进展和发展的理论李群，离散子群和齐次空间。在过去的三十年里，这一领域取得了令人瞩目的进展，突出了动力系统和遍历理论、丢番图近似、刚性理论、离散数学等的各种联系。然而，自21世纪初以来，没有举行过统一这一主题和相关领域的重大国际会议。这证明有必要召开计划中的会议，该会议将使这些领域的世界领导人聚集一堂，并作为传播新成果、方法和想法的论坛。 暂定的题目包括：高秩李群和格作用的刚性和分类;格作用的遍历定理;线性群的增长性质和Tits替代;齐次簇上整数点的计数;高秩阿贝尔作用的刚性度量和量子唯一遍历性; Littlewoods猜想的例外集;在具有依赖量的丢番图逼近中的应用; Teichmueller空间上作用的不变测度及其在台球中的应用。

AbstractLubotzkyThis award provides partial support for a four-day international conference to cover recent progress and developments of the theory of Lie groups, discrete subgroups and homogeneous spaces. The last three decades have brought spectacular advances in the area, highlighting various connections to dynamical systems and ergodic theory, Diophantine approximation, rigidity theory, discrete mathematics etc. The progress has been especially rapid and impressive during several recent years. However, no major international conferences unifying this subject and related fields were held since the beginning of the 21st century. This justifies the need for the planned conference, which is going to bring together world leaders in these fields and serve as a forum for dissemination of new results, methods and ideas. Tentative list of topics includes: rigidity and classification of actions of higher rank Lie groups and lattices; ergodic theorems for lattice actions; growth properties of linear groups and Tits alternative; counting integer points on homogeneous varieties; measure rigidity of higher rank abelian actions and quantum unique ergodicity; the set of exceptions to Littlewoods conjecture; applications to Diophantine approximation with dependent quantities; invariant measures for actions on the Teichmueller space and applications to billiards.