Conference: Geometric and Asymptotic Group Theory with Applications 2023

该奖项为将于7月17-21日在奥地利维也纳的Erwin Schroedinger研究所举行的“几何与渐近群论及其应用2023”会议的美国参会者提供支持。这次会议是由Pi Kim Ruane与Christopher Cashen(维也纳大学)、Sangyun Kim(韩国高级科学与技术研究所)和Yash Lodha(夏威夷大学)合作举办的。这是第16版的年度系列赛，之前的迭代已经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的研究人员与动力学和离散概率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，并引发新的互动。会议将举行全体会议，并举行公开问题讨论会。组织者计划有针对性的招聘过程，以扩大这些领域传统上代表性不足的群体的参与。会议的主题包括随机行走和边界、遍历理论方法和动力学起源组。会议将举行三次全体会议。第一部分将集中于几何和离散概率之间的相互作用，以及在随机游动、渗流和统计力学的伊辛模型中的应用。第二项涉及与气候科学家一起应用建筑物的几何形状和对单元格建筑群的集体行动，实施用于气候模拟和天气预报的计算机程序包。第三讲将讨论组合曲率在几何网络结构分析中的应用。群上随机游动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Martin和Gromov边界的等价性，这种关系对于双曲群类是明确的。在双曲群之外探索这种关系导致了新的边界概念的构建，这将在这次会议上讨论。从流形的经典背景出发的遍历理论概念和定理才刚刚开始被更一般的空间和群所理解。即使在双曲的情况下，仍然有大量的工作与遍历理论、群论和几何不变量相关。最后，动力起源的群最近提供了无限群的新例子，解决了该地区长期悬而未决的问题。会议还将讨论这些例子以及今后的研究方向。活动网页位于https://sites.google.com/view/gagta2023.This奖，反映了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 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.