Conference: Geometric and Asymptotic Group Theory with Applications 2023

会议：几何和渐近群理论及其应用 2023

• 批准号: 2311110
• 负责人: Kim Ruane
• 金额: $ 1.6万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311110&HistoricalAwards=false
• 关键词: Conference; Geometric; Asymptotic; Group; Theory; Conference; Geometric; Asymptotic; Group; Theory

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.