Abstract: In this talk, we will discuss various properties of asymptotic translation lengths of pseudo-Anosov elements of mapping class groups on curve complex. In particular, we will discuss the asymptotic behavior of minimal asymptotic translation lengths of mapping class group and its subgroups. If time permits, I will describe the relation between the asymptotic translation length of pseudo-Anosov elements and Thurston's fibered cone of hyperbolic 3-manifolds. T

his is joint work with Hyungryul Baik, Eiko Kin, and Chenxi Wu.