Homin Lee
June E Huh fellow
KIAS (Korea Institute for Advanced Study)
E-mail: hominlee (at) kias (dot) re (dot) kr
E-mail: hominlee (at) kias (dot) re (dot) kr
I am a June E Huh Fellow at June E Huh Center for Mathematical Challenges (HCMC) at Korea Institute for Advanced Study (KIAS) since July 2025. I was a Boas Assistant Professor (postdoc) in the Mathematics department at Northwestern University 2022-2025. Previously, I was a graduate student in the Mathematics department at Indiana University Bloomington, under the supervision of David Fisher.
Here is my CV. My papers, preprints, and works in progress can be found below.
You can also see ''Conference and Seminar Organizations'', ''Selected talks'', and ''Teaching and Mentoring'' in each page.
I am broadly interested in geometry, groups, and dynamics. Currently my work focuses on (non-uniform and uniform) hyperbolic dynamics and smooth ergodic theory with their applications on rigidity of lattices including the Zimmer Program (see, also, here).
I am especially interested in exploring
Rigidity in geometry and dynamical systems such as smooth actions on manifolds by (discrete) groups,
Algebraic and arithmetic properties of discrete subgroups of Lie groups (such as arithmetic groups) and their geometric and number theoretic applications, and
Dynamics in Low dimensional geometry and topology.
Rigidity theorems for higher rank lattice actions, Geometric and Functional Analysis (GAFA), Vol 34, pages 1114-1170, 2024
Global rigidity of higher rank lattice actions with dominated splitting, Ergodic Theory and Dynamical Systems. (ETDS) 2024;44(3):799-828. doi:10.1017/etds.2023.31.
A height gap in GLd(Q) and almost laws, Groups, Geometry, and Dynamics (GGD) 19 (2025), no. 3, pp. 899–912. Joint with Lvzhou Chen and Sebastian Hurtado.
Pressure metrics in geometry and dynamics, available at https://arxiv.org/abs/2407.18441, to appear Proceedings volume for the Shishikura conference. Joint with Yan Mary He and Insung Park.
Positive entropy actions by higher rank lattices, available at https://arxiv.org/abs/2409.05991, submitted. Joint with Aaron Brown.
Partially hyperbolic lattice actions on 2-step nilmanifolds, available at https://arxiv.org/abs/2410.00784, submitted. Joint with Sven Sandfeldt.
Absolute continuity of stationary measures, available at https://arxiv.org/abs/2409.18252, preprint. Joint with Aaron Brown, Davi Obata, and Yuping Ruan.
Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric, available at https://arxiv.org/abs/2507.17077, submitted. Joint with Yan Mary He and Insung Park.
Singularity of Furstenberg measure for infinite covolume discrete subroups in higher rank, available at https://arxiv.org/abs/2508.06329, preprint. Joint with Wouter van Limbeek and Giulio Tiozzo.
*ArXiv versions may differ significantly from the published version.
*I expect these papers will be available before the end of 2025.
Absolute continuity of stationary measures for random surface dynamics, in preparation, Joint with Aaron Brown, Davi Obata, and Yuping Ruan.
Abstract: We find conditions for stationary measures of random dynamical systems having dissipative diffeomorphisms to be absolutely continuous on surfaces. These conditions involve an uniformly expanding on average property in the future (UEF) and past (UEP). Applications of our results include random dynamical systems generated by perturbations of volume preserving surface diffeomorphisms, verifying UEF and UEP. We also obtained an orbit classification and equidistribution results. The paper considers much more general settings (non-uniform hyperbolicity) than we consider in previous paper, "Absolutely continuity of stationary measures".
Exact dimensionality of hyperbolic stationary measures, in preparation, Joint with Aaron Brown.
Abstract: We show the exact dimensionality of hyperbolic stationary measures for random dynamical systems generated by a finite entropy drift measure supported on C2 diffeomorphisms.
Surface diffeomorphisms with smooth measure of maximal entropy, in preparation, Joint with Aaron Brown.
Abstract: We provide many "flexible" examples of diffeomorphisms that has a unique smooth measure of maximal entropy on surfaces other than torus, sphere, projective space, and Klein bottle.
Rigidity of higher rank product systems (tentative title), in preparation, Joint with Sven Sandfeldt and Kurt Vinhage
Abstract: We showed a perturbation of various product of algebraic hyperbolic higher rank free abelian group actions and isometric actions on circle is still given by a product action.
Last update: October 01, 2025