Hee Oh

About

Hee Oh is the Abraham Robinson Professor of Mathematics at Yale University, specializing in group actions and dynamics. Her research focuses on the dynamics and rigidity of discrete subgroups in higher rank Lie groups, Anosov groups, and hyperbolic manifolds. She has made significant contributions to the understanding of limit cones, critical exponents, and growth indicators of coamenable normal subgroups, as well as the ergodic theory and geometric structures of hyperbolic spaces. Her work often explores the interplay between geometric group theory, ergodic theory, and number theory, with applications to counting problems, spectral theory, and rigidity phenomena. She has collaborated extensively with other mathematicians on topics such as conformal measures, horospherical actions, and the dynamics of Kleinian groups, contributing to the advancement of knowledge in these areas through numerous publications and preprints.

Research topics

• Combinatorics
• Composite material
• Geometry
• Mathematics
• Pure mathematics
• Mathematical analysis
• Materials science
• Statistics
• Chemical engineering
• Chemistry

Selected publications

• Invariant Measures for Horospherical Actions and Anosov Groups

  International Mathematics Research Notices · 2022 · 28 citations

  Senior authorCorresponding

  Abstract Let $\Gamma $ be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $\Gamma \backslash G$, up to proportionality, is homeomorphic to ${\mathbb {R}}^{\text {rank}\,G-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup that normalizes $N$. One of the main ingredients is to…

  DOI

• Tent property of the growth indicator functions and applications

  Geometriae Dedicata · 2023-11-14 · 7 citations

  articleSenior author
  PublisherDOI

• Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends

  Geometry & Topology · 2024-11-25 · 6 citations

  articleOpen accessSenior author

  We establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\operatorname{SO}(d,1)$ acting on the space $\Gamma\backslash \operatorname{SO}(d,1)$, assuming that the associated hyperbolic manifold $M=\Gamma\backslash \mathbb H^d$ is a convex cocompact manifold with Fuchsian ends. For $d=3$, this was proved earlier by McMullen, Mohammadi and Oh. In a higher dimensional case, the possibility of accumulation on closed orbits of int…

  PublisherOA PDFDOI

• Ergodic dichotomy for subspace flows in higher rank

  Communications of the American Mathematical Society · 2025-02-19 · 3 citations

  articleOpen access

  In this paper, we study the ergodicity of a one-parameter diagonalizable subgroup of a connected semisimple real algebraic group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acting on a homogeneous space or, more generally, a homogeneous-like space, equipped with a Bowen-Marguli…

  PublisherOA PDFDOI

• On denseness of horospheres in higher rank homogeneous spaces

  Ergodic Theory and Dynamical Systems · 2024-02-19 · 2 citations

  articleOpen accessSenior author

  Abstract Let $ G $ be a connected semisimple real algebraic group and $\Gamma &lt;G$ be a Zariski dense discrete subgroup. Let N denote a maximal horospherical subgroup of G , and $P=MAN$ the minimal parabolic subgroup which is the normalizer of N . Let $\mathcal E$ denote the unique P -minimal subset of $\Gamma \backslash G$ and let $\mathcal E_0$ be a $P^\circ $ -minimal subset. We consider a notion of a horospherical limit point in the Furstenberg boundary $ G/P $ and show that the following…

  PublisherOA PDFDOI

Recent grants

• Thin Groups and Dynamics

  NSF · $600k · 2014–2019

• Dynamics and Kleinian Groups

  NSF · $531k · 2019–2025

• Equidistribution on homogeneous spaces for orbits of discrete groups beyond lattices

  NSF · $204k · 2011–2013

Frequent coauthors

• Minju Lee

  34 shared

• Amir Mohammadi

  30 shared

• Nimish A. Shah

  25 shared

• Alex Kontorovich

  18 shared

• Dongryul M. Kim

  16 shared

• Yves Benoist

  13 shared

• S. F. Edwards

  13 shared

• Dale Winter

  Winchester Hospital

  10 shared

Labs

• Hee Oh LabPI

Education

• Ph. D, Mathematics

  Yale

  1997

Similar researchers at Yale University

• Ronald Coifmanh-74
• Vladimir Rokhlinh-60
• Dan Spielmanh-57