Lie Groups: Dynamics, Rigidity, Arithmetic

摘要Lubotzky 该奖项为为期四天的国际会议提供部分支持，会议涵盖李群、离散子群和齐次空间理论的最新进展和发展。过去三十年来，该领域取得了惊人的进展，突出了与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。近年来，进展尤其迅速和令人印象深刻。然而，进入21世纪以来，还没有召开过将该学科与相关领域统一起来的大型国际会议。这证明了计划中的会议的必要性，该会议将汇集这些领域的世界领导人，并作为传播新成果、方法和想法的论坛。 暂定主题列表包括：高阶李群和格的刚性和作用分类；格子作用的遍历定理；线性群和Tits替代的生长特性；计算同质品种的整数点；测量更高阶阿贝尔行为的刚性和量子独特的遍历性；利特伍德猜想的一组例外；具有相关量的丢番图近似的应用； Teichmueller 空间上的动作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.