Hee Oh
Abraham Robinson Professor of Mathematics
Paper mail Department of Mathematics
10 Hillhouse Ave.
Yale University
New Haven, CT 06520
E-mail hee.oh(AT)yale(DOT)edu
Phone (203) 432-4193 (office)
Fax (203) 432-7316
Office 212B LOM

Curriculum Vitae

In press

Article in American Scientist by Dana Mackenzie on Apollonian gasket


ICWM Plenary lecture(2014)
Extended version of my ICM lecture (2010)

Preprints and publications

Some papers below can be slightly different from their printed versions. Please refer to the numbering from the printed versions. For the link to my papers in MathSciNet, click here.
  1. Invariant measures for horospherical actions and Anosov groups.
    (with M. Lee), Preprint (pdf)
  2. Anosov groups: local mixing, counting, and equidistribution.
    (with S. Edwards and M. Lee), Preprint, 49 pages (pdf)
  3. Isolations of geodesic planes in the frame bundle of a hyperbolic 3-manifold.
    (with A. Mohammadi), Preprint, 43 pages (pdf)
  4. Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds.
    (with S. Edwards), Preprint, 30 pages (pdf)
  5. Dynamics for discrete subgroups of SL(2,C).
    Preprint, 46 pages (14 figures), survey article, to appear in Margulis volume (pdf)
  6. Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1).
    (with M. Lee), Journal of Modern Dynamics, Vol 15 (2019), 263--276 (pdf)
  7. Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends.
    (with M. Lee), Preprint, 101 pages (pdf)
  8. Exponential mixing and shrinking targets for geodesic flow on geometrically finite hyperbolic manifolds.
    (with D. Kelmer), Preprint, 36 pages (pdf)
  9. Orbit closures for the PSL(2,R)-action on hyperbolic 3-manifolds (Fields Institute Summer School Lecture Notes).
    Preprint (pdf)
  10. Geodesic planes in geometrically finite acylindrical 3-manifolds.
    (with Y. Benoist), Preprint, 39 pages, submitted to a special memorial volume for A. Katok in ETDS (pdf)
  11. Geodesic planes in the convex core of an acylindrical 3-manifold.
    (with C. McMullen and A. Mohammadi), Preprint, 32 pages (pdf)
  12. Local mixing and invariant measures for horospherical subgroups on abelian covers.
    (with W. Pan), IMRN 2019, Issue 19, 6036-6088 (pdf)
  13. Prime number theorems and holonomies for hyperbolic rational maps
    (with D. Winter), Inventiones Mathematicae, Vol 208 (2017), 401--440 (pdf)
  14. Horocycles in hyperbolic 3-manifolds
    (with C. McMullen and A. Mohammadi), GAFA, Vol 26 (2016), 961--973 (pdf)
  15. Geodesic planes in hyperbolic 3-manifolds
    (with C. McMullen and A. Mohammadi), Inventiones Mathematicae, Vol 209 (2017), 425--461 (pdf)
  16. Invariant Radon measures for unipotent flows and products of Kleinian groups
    (with A. Mohammadi), PAMS. 146 (2018), 1469--1479 (pdf)
  17. Fuchsian groups and compact hyperbolic surfaces
    (with Y. Benoist), L'Enseignement Mathématique, Vol 62 (2016), 189--198 (pdf)
  18. Uniform congruence counting for Schottky semigroups in SL_2(Z)
    (with M. Magee and D. Winter), J. Reine Angew. Math., Vol 753 (2019), 89--135 (pdf)
  19. Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z)
    (with D. Winter), Journal of the AMS, Vol 29 (2016), 1069--1115 (pdf)
  20. Closed geodesics and holonomies for Kleinian manifolds
    (with G. Margulis and A. Mohammadi), GAFA, Vol 24 (2014), 1608--1636 (pdf)
  21. Classification of joinings for Kleinian groups
    (with A. Mohammadi), Duke Math.J., Vol 165 (2016), 2155--2223 (pdf)
  22. Matrix coefficients, counting and primes for orbits of geometrically finite groups
    (with A. Mohammadi), Journal of the EMS, Vol 17 (2015), 837--897 (pdf)
  23. Ergodicity of unipotent flows and Kleinian groups
    (with A. Mohammadi), Journal of the AMS, Vol 28 (2015), 531--577 (pdf)
  24. Eigenvalues of congruence covers of geometrically finite hyperbolic manifolds
    Journal of Geometric Analysis, Vol 25 (2015), 1421--1430 (pdf)
  25. Counting visible circles on the sphere and Kleinian groups
    (with N. Shah), LMS series Vol 425, 272--288. (pdf)
  26. Apollonian circle packings: dynamics and number theory
    Japanese Journal of Math., Vol 9 (2014), 69--97, (expanded version of the 13th Takagi Lecture series notes). (pdf)
  27. Harmonic analysis, ergodic theory and counting for thin groups
    In "Thin groups and superstrong approximation", MSRI publ.61 Cambridge Univ. Press. 2014 (pdf)
  28. Limits of translates of divergent geodesics and integral points on one-sheeted hyperboloids
    (with N. Shah), Israel J. Math., Vol 199 (2014), pp. 915--931 (pdf)
  29. Effective circle count for Apollonian packings and closed horospheres
    (with M. Lee), GAFA, Vol 23 (2013), 580--621 (pdf)
  30. Equidistribution and counting for orbits of geometrically finite hyperbolic groups
    (with N. Shah), Journal of the AMS, Vol 26 (2013), 511--562 (pdf)
  31. The asymptotic distribution of circles in the orbits of Kleinian groups
    (with N. Shah), Inventiones Mathematicae, Vol 187 (2012), 1--35 (pdf)
  32. On the distribution of orbits of geometrically finite hyperbolic groups on the boundary
    (with S. Lim), Ergod. Th. & Dynam. Sys., Vol 32, 173--189 (2012) (pdf)
  33. Almost prime Pythagorean triples in thin orbits
    (with A. Kontorovich), J. Reine Angew. Math. Vol 667 (2012), 89--131 (pdf)
  34. Effective equidistribution of S-integral points on symmetric varieties
    (with Y. Benoist), Annales de L'Institut Fourier, Vol 62 (2012), 1889--1942 (pdf )
  35. Apollonian circle packings and closed horospheres on hyperbolic 3 manifolds
    (with A. Kontorovich), Journal of the AMS. 24 (2011), 603--648 (pdf)
  36. Rational points on homogeneous varieties and equidistribution of adelic periods
    (with A. Gorodnik), GAFA, Vol 21 (2011), 319--392 (pdf)
  37. Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond
    Proceedings of International Congress of Mathematicians (2010), Vol III, 1308--1331 (pdf)
  38. Discreteness criterion for subgroups of products of SL(2)
    (with Y. Benoist), Transformation Groups, Vol 15 (2010), 503--515 (pdf)
  39. Orbital counting via mixing and unipotent flows
    in Homogeneous flows, Moduli Spaces and Arithmetic, Clay Mathematics Proceedings, 2010, Vol 10, 339--375 (pdf)
  40. Strong wavefront lemma and counting lattice points in sectors
    (with A. Gorodnik and N. Shah), Israel J. Math., Vol 176 (2010), 419--444 (pdf)
  41. Discrete subgroups of SL_3(R) generated by triangular matrices
    (with Y. Benoist), Int. Math. Res. Notices, Article ID 149, 2009 (pdf)
  42. Integral points on symmetric varieties and Satake compactifications
    (with A. Gorodnik and N. Shah), American J. Math., Vol 131 (2009), 1--57 (pdf)
  43. Manin's and Peyre's conjectures on rational points and adelic mixing
    (with A. Gorodnik and F. Maucourant), Ann. Sci. Ecole Norm. Sup. Vol 41 (2008) 47--97 (pdf)
  44. Polar decomposition for p-adic symmetric spaces
    (with Y. Benoist), Int. Math. Res. Notices (2007), Article ID 121 (pdf)
  45. Equidistribution of rational matrices in their conjugacy classes
    (with Y. Benoist), Geom. and Funct. Analysis, Vol 17 (2007) (pdf)
  46. Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
    (with A. Gorodnik), Duke Math. J. Vol 139 (2007), 483--525 (pdf)
  47. Representations of integers by an invariant polynomial and unipotent flows
    (with A. Eskin), Duke Math. J., Vol 135 (2006), 481--506 (pdf)
  48. Ergodic theoretic proof of equidistribution of Hecke points
    (with A. Eskin), Erg. The & Dyn. Sys, Vol 26 (2006), 163--167 (pdf)
  49. On uniform exponential growth for linear groups
    (with A. Eskin and S. Mozes), Inventiones Math. Vol 160 (2005), 1--30 (pdf)
  50. Lattice action on finite volume homogeneous spaces
    J. Korean Math. Soc., Vol 42 (2005), 635--653 (pdf)
  51. The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group
    Israel J. Math (Furstenberg volume), Vol 149 (2005), 301--316 (pdf)
  52. On a problem concerning arithmeticity of discrete groups acting on H...H
    in "Algebraic groups and Arithmetic" (TIFR, India) (pdf)
  53. Harmonic analysis and Hecke operators
    in "Rigidity in Dynamics and Geometry", Springer-Verlag, edited by Burger and Iozzi (pdf)
  54. Hardy-Littlewood system and representations of integers by an invariant polynomial
    Geom. and Funct. Analysis, Vol 14 (2004) 791--809 (pdf)
  55. Finiteness of compact maximal flats of bounded volume
    Ergod. Th and Dynam. Sys. Vol 24 (2004), 217--225 (pdf)
  56. Cartan decomposition subgroups of SO(2,n)
    (with D. Witte), Trans. AMS Vol 356 (2004) 1--38 (pdf)
  57. Equidistribution of integer points on a family of homogeneous varieties: a problem of Linnik
    (with W. Gan), Compositio Math. Vol 136 (2003), 323--352 (pdf)
  58. Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
    Duke Math. J., vol 113 (2002), pp. 133--192 (pdf)
  59. Uniform exponential growth for linear groups (announcement)
    (with A. Eskin and S. Mozes) Int. Math. Res. Not. no 31 (2002), 1675--1683
  60. Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
    (with D. Witte), Geom. Dedicata, vol 89 (2002), 25–57 (pdf)
  61. Hecke operators and equidistribution of Hecke points
    (with L. Clozel and E. Ullmo), Inventiones Math., vol 144 (2001), pp. 327--351 (pdf)
  62. Adelic version of Margulis arithmeticity theorem
    Math. Ann. vol 321 (2001), 4, pp. 789--815 (pdf)
  63. New examples of compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
    (with Dave Witte), IMRN, 2000, no 5, pp. 235--251 (pdf)
  64. S-arithmeticity of discrete subgroups containing lattices in horospherical subgroups
    Duke Math. J., vol 101 (2000), pp. 209--219
  65. On discrete subgroups containing a lattice in a horospherical subgroup
    Israel J. of Math., vol 110 (1999), pp. 333--340 (pdf)
  66. Tempered subgroups and representations with minimal decay of matrix coefficients
    Bull. Math. Soc. France, vol 126 (1998), pp. 355--380 (pdf) Minor correction: (pdf)
  67. Discrete subgroups generated by lattices in opposite horospherical subgroups
    J. Algebra, vol 203 (1998), pp. 621--676 (pdf)
  68. Arithmetic properties of some Zariski dense subgroups
    Proceedings of International Colloquium on "Lie groups and Ergodic theory" in TIFR, Bombay, 1996
  69. Discrete subgroups of SL_n(R) generated by lattices in horospherical subgroups
    C. R. Acad. Sci. Paris, Series I, vol 323 (1996), pp. 1219--1224 (pdf)