ICTS:31228

Video URL

Estimating the distances between hyperbolic structures in the moduli space

Estimating the distances between hyperbolic structures in the moduli space

(2025). Estimating the distances between hyperbolic structures in the moduli space. SciVideos. https://youtube.com/live/aWIC6ipB7oQ

Estimating the distances between hyperbolic structures in the moduli space. SciVideos, Feb. 26, 2025, https://youtube.com/live/aWIC6ipB7oQ 

          @misc{ scivideos_ICTS:31228,
            doi = {},
            url = {https://youtube.com/live/aWIC6ipB7oQ},
            author = {},
            keywords = {},
            language = {en},
            title = {Estimating the distances between hyperbolic structures in the moduli space},
            publisher = {},
            year = {2025},
            month = {feb},
            note = {ICTS:31228 see, \url{https://scivideos.org/index.php/icts-tifr/31228}}
          }
Kashyap Rajeevsarathy
Talk numberICTS:31228
Source RepositoryICTS-TIFR
Collection

Abstract

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. Given a finite subgroup $H$ of $\mathrm{Mod}(S_g)$, let $\mathrm{Fix}(H)$ be the set of all fixed points induced by the action of $H$ on the Teichm\"{u}ller space $\mathrm{Teich}(S_g)$ of $S_g$. We will discuss a method to estimate the distance between the unique fixed points of certain irreducible cyclic actions on $S_g$. We begin by deriving an explicit description of a pants decomposition of $S_g$, the length of whose curves are bounded above by the Bers' constant. We will then use the quasi-isometry between $\mathrm{Teich}(S_g)$ and the pants graph $\mathcal{P}(S_g)$ to estimate the distance.