Conference: Geometric and Asymptotic Group Theory with Applications 2023

该奖项为“几何和渐近群论及其应用2023”会议的美国参与者提供支持，该会议将于7月17日至21日在奥地利维也纳的Erwin Schroedinger研究所举行。此次会议由PI Kim Ruane和Christopher Cashen（维也纳大学）、Sangyun Kim（韩国科学技术院）、Yash Lodha（夏威夷大学）共同主办。这是该年度系列的第16届，之前的几届已在四大洲的十个不同国家举行。会议的目标是将无限群论的组合、渐近和几何方面的早期职业和成熟研究人员与动力学和离散概率方面的研究人员聚集在一起，巩固基于这些学科之间相互作用的最新进展，并激发新的相互作用。会议将以全体会议和公开问题讨论会为特色。组织者计划进行有针对性的招聘过程，以扩大传统上在这些领域代表性不足的群体的参与。会议的主题包括随机漫步和边界、遍历理论方法和动力起源组。会议将举行三次全体会议。第一部分将关注几何和离散概率之间的相互作用，以及随机游走、渗透和统计力学的伊辛模型的应用。第二项涉及建筑几何的应用和气候科学家在细胞复合体上的群体行动，在实施用于气候模拟和天气预报的计算机包中。第三讲将讨论组合曲率在几何网络结构分析中的应用。群上随机漫步的概率性质揭示了几何性质和代数性质之间的密切关系。通过马丁边界和格罗莫夫边界的等价性，对双曲群的类表明了这种关系。在双曲群类之外探索这种关系导致了新的边界概念的构建，这将在本次会议上讨论。流形经典集合的遍历理论概念和定理才刚刚开始被理解为更一般的空间和群。即使在双曲情况下，关于遍历论、群论和几何不变量的研究仍有许多工作要做。最后，动力起源群最近提供了无限群的新例子，解决了该领域长期存在的开放性问题。这些例子以及未来的研究方向也将在会议上讨论。该活动的网页在https://sites.google.com/view/gagta2023.This。奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

This award provides support for the U.S.-based participants of the conference “Geometric and Asymptotic Group Theory with Applications 2023” that will take place July 17-21 at the Erwin Schroedinger Institute, Vienna, Austria. The conference is organized by the PI Kim Ruane in collaboration with Christopher Cashen (University of Vienna), Sangyun Kim (Korea Advanced Institute of Science & Technology), and Yash Lodha (University of Hawaii). This is the 16th edition of an annual series, previous iterations of which have been held in ten different countries on four continents. The goal of the conference is to bring together both early career and established researchers in combinatorial, asymptotic, and geometric aspects of infinite group theory together with researchers in dynamics and discrete probability, to consolidate recent advances based on the interplay between these subjects and to spark new interactions. The conference will feature plenary talks and a discussion session of open problems. Organizers plan a targeted recruitment process to broaden participation among groups that are traditionally underrepresented in these fields. The topics of the conference include random walks and boundaries, ergodic-theoretic methods, and groups of dynamical origins. The conference will feature three plenary talks. The first will focus on interactions between geometry and discrete probability with applications to random walks, percolation, and the Ising modeling of statistical mechanics. The second involves applications of the geometry of buildings and group actions on cell complexes with climate scientists, in the implementation of the computer package that is used in climate simulation and weather prediction. The third talk will cover applications of combinatorial curvature to analyze the structure of geometric networks. Probabilistic properties of random walks on groups reveal a close relationship between geometric and algebraic properties. This relationship has been made explicit for the class of hyperbolic groups via the equivalence of the Martin and Gromov boundaries. Exploring this relationship outside the class of hyperbolic groups has resulted in the construction of new notions of boundaries that will be discussed at this conference. Ergodic-theoretic notions and theorems from the classical setting of manifolds have just begun to be understood for more general spaces and groups. Much work remains in relating ergodic-theoretic, group-theoretic, and geometric invariants even in the hyperbolic case. Finally, groups of dynamical origin have recently provided new examples of infinite groups that settle long-standing open problems in the area. Those examples as well as future directions for study will be discussed at the conference as well. The event webpage is at https://sites.google.com/view/gagta2023.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.