ICTS:29093

Video URL

Growth of (sub)groups with hyperbolicity - 1

Growth of (sub)groups with hyperbolicity - 1

(2024). Growth of (sub)groups with hyperbolicity - 1. SciVideos. https://youtube.com/live/-jJPZYvz7X0

Growth of (sub)groups with hyperbolicity - 1. SciVideos, Jul. 30, 2024, https://youtube.com/live/-jJPZYvz7X0 

          @misc{ scivideos_ICTS:29093,
            doi = {},
            url = {https://youtube.com/live/-jJPZYvz7X0},
            author = {},
            keywords = {},
            language = {en},
            title = {Growth of (sub)groups with hyperbolicity - 1},
            publisher = {},
            year = {2024},
            month = {jul},
            note = {ICTS:29093 see, \url{https://scivideos.org/icts-tifr/29093}}
          }
Inhyeok Choi
Talk numberICTS:29093
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

In geometric group theory, a group is studied via its action on some metric spaces, often with unbounded orbit. It is then natural to investigate the growth of orbit points, group elements, and conjugacy classes. Furthermore, the pioneering works of Patterson and Sullivan and subsequent development connected this growth problem with the dynamics on the boundary and the geodesic flow on the space. In this mini-course, we will study the growth problem in hyperbolic groups and CAT(0) groups via a combinatorial approach. The flexible nature of our approach allows many generalizations.

In week 2, we will compute the growth rate of certain subsets/subgroups of the ambient group. For example, refer to the following articles:
 1. I. Gekhtman and W. Yang, Counting conjugacy classes in groups with contracting elements. (2022)
 2. V. Erlandsson and J. Souto, Counting geodesics of given commutator length. (2023)

Basic references:

Introduction to hyperbolic groups, by Davide Spriano h...