Conference: Geometric and Asymptotic Group Theory with Applications 2023

该奖项为美国提供支持-基于会议的参与者“几何和渐近群理论与应用2023”，将于7月17日至21日在欧文薛定谔研究所，维也纳，奥地利。会议由PI Kim Ruane与Christopher Cashen（维也纳大学），Sangyun Kim（韩国科学技术高级研究所）和Yash Lodha（夏威夷大学）合作组织。这是该年度系列的第16版，之前的迭代已在四大洲的十个不同国家举行。会议的目标是将无限群理论的组合，渐近和几何方面的早期职业和既定研究人员与动力学和离散概率的研究人员聚集在一起，以巩固基于这些主题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和讨论悬而未决的问题。组织者计划开展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游走和边界，遍历理论方法，和群体的动力起源。会议将举行三次全体会议。第一个将集中在几何和离散概率之间的相互作用与应用随机游走，渗流，和统计力学的伊辛建模。第二个项目涉及应用建筑物的几何形状和与气候科学家一起在细胞复合体上的群体行动，以实施用于气候模拟和天气预测的计算机包。第三个讲座将涵盖组合曲率的应用，以分析几何网络的结构。 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。这种关系已经明确的类双曲群通过等价的马丁和格罗莫夫边界。在双曲群之外探索这种关系，导致了新的边界概念的构建，这些概念将在本次会议上讨论。在更一般的空间和群中，来自经典流形的遍历理论概念和定理才刚刚开始被理解。许多工作仍然在有关遍历理论，群论，几何不变量，甚至在双曲的情况下。 最后，群体的动力起源最近提供了新的例子，解决长期悬而未决的问题，在该地区的无限群。这些例子以及未来的研究方向也将在会议上讨论。该活动的网页是在https://sites.google.com/view/gagta2023.This奖反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的知识价值和更广泛的影响审查标准的支持。

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.