The Dynamics and Arithmetic Structures on Manifolds (DASOM) Center is devoted to developing new theoretical frameworks for understanding arithmetic structures on manifolds. Manifolds play a central role in modern mathematics, unifying geometry, number theory, and dynamical systems. By integrating ideas from these areas, the Center seeks to uncover fundamental mechanisms governing arithmetic and geometric phenomena on manifolds.
A primary focus of the Center is the study of group actions on manifolds from arithmetic and dynamical viewpoints. We investigate how fundamental groups of manifolds arise as subgroups of arithmetic groups, and how this perspective enables deep analysis using tools from number theory, including Iwasawa theory, and from arithmetic and homogeneous dynamics. This approach reveals intrinsic arithmetic features of manifolds that go beyond purely geometric methods.
Dynamics of group actions form a central theme of our research. We explore a wide range of settings, including homogeneous dynamics, actions of lattice groups, and actions of mapping class groups. These dynamical investigations provide powerful tools for understanding the arithmetic structure of fundamental groups, as well as the computability and structural properties of arithmetic representations.
The Center also studies moduli spaces that parametrize arithmetic and geometric structures on manifolds. By examining their geometry, topology, and dynamics, we aim to understand how arithmetic information is encoded in these spaces. Through the interaction of arithmetic manifolds, group dynamics, and moduli theory, the DASOM Center seeks to build new bridges across disciplines and to advance a coherent research program in arithmetic geometry and dynamics.
Professors: Gye-Seon Lee, Junho Peter Whang, Dohyeong Kim, and Seonhee Lim
Post-doctoral fellows: Michael Bersudsky, Nadav Gropper
Associate post-doctoral fellows: Jungwon Lee (MPI-Bonn), Kyeongro Kim (KIAS), Hongtaek Jung (KIAS),
Graduate students: Seunghoon Hwang, Heecheol Kwon, Dong Hyun Lee, Jaeyoung Kim, Minchang Kim, Seongmin Kim, Kangrae Park, Kwansoo Kim, Jun Seok Byeon, Donghyun Gwag, Seongyoun Kim, Young Kyun Kim, Eungchan Kim, Jihye Oh, Young Joon Ley
Staff: Haeja Oh (e-mail: ysh8010@snu.ac.kr)