Research Focus
Geometric group theory, Measured group theory
I study groups and metric spaces that appear in geometric group theory and low-dimensional topology. I try to reveal the geometry of groups by looking at the dynamics of their actions on various spaces. I also study some notions from adjacent fields for this purpose, such as random walks on groups, entropy of dynamical systems and length spectra of manifolds.
Publications
- Confine subgroups in groups with contracting elements. With Ilya Gekhtman, Wenyuan Yang and Tianyi Zheng. Preprint, arXiv:2405.09070
- Random walks and contracting elements I: Deviation inequality and limit laws. Preprint, arXiv:2207.06587
- Pseudo-Anosovs are exponentially generic in mapping class groups. To appear in Geometry & Topology, arXiv:2110.06678
- Central limit theorem and geodesic tracking on hyperbolic spaces and Teichmüller spaces. Advances in Mathematics, Vol. 431 (2023), 109236
- Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces. With Hyungryul Baik and Dongryul M. Kim. JIMJ.