Hee Oh

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

In press

Article in American Scientist by Dana Mackenzie on Apollonian gasket

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.

Preprint

  1. Expanding maps and Continued fractions
    (with Michael Magee and Dale Winter). (pdf)
  2. Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z)
    (with Dale Winter), As of Dec 2. ArXiv:1410.4401 (pdf)
  3. Classification of joinings for Kleinian groups
    (with Amir Mohammadi) arXiv:1404.1510 (pdf)

Accepted for Publication

  1. Ergodicity of unipotent flows and Kleinian groups
    (with Amir Mohammadi) arXiv:1112.4024. To appear in Journal of AMS. (pdf)
  2. Matrix coefficients, Counting and Primes for orbits of geometrically finite groups
    (with Amir Mohammadi) arXiv:1208.4139 To appear in Journal of European Math. Society (pdf)
  3. Eigenvalues of congruence covers of geometrically finite hyperbolic manifolds
    arXiv:1302.2950 To appear in Journal of Geometric Analysis (pdf)
  4. Counting visible circles on the sphere and Kleinian groups
    (with Nimish Shah) To appear in Proceedings of the conference on "Geometry, Topology and Dynamics in negative curvature" to be published by the LMS Lecture series. (pdf)

Published

  1. Closed geodesics and holonomies for Kleinian manifolds
    (with Gregory Margulis and Amir Mohammadi) GAFA, Vol 24 (2014), 1608–1636 (pdf)
  2. Apollonian circle packings: Dynamics and Number theory
    Japanese Journal of Math., Vol 9 (2014), 69–97, Based on the 13th Takagi Lecture series, given in 2013. (pdf)
  3. Harmonic analysis, Ergodic theory and Counting for thin groups
    In "Thin groups and superstrong approximation", edited by Breuillard and Oh, Math. Sci.Res.Inst.Publ. 61, Cambridge Univ. Press. Cambridge 2014 (pdf)
  4. Limits of translates of divergent geodesics and integral points on one-sheeted hyperboloids
    (with Nimish Shah) Israel J. Math., Vol 199 (2014), pp. 915–931 (pdf)
  5. Effective circle count for Apollonian packings and closed horospheres
    (with Min Lee), GAFA, Vol 23 (2013), 580–621 (pdf)
  6. Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
    (with Nimish Shah), Journal of AMS, Vol 26 (2013), 511–562 (pdf)
  7. The asymptotic distribution of circles in the orbits of Kleinian groups
    (with Nimish Shah) Inventiones Mathematicae, Vol 187 (2012), 1–35 (pdf)
  8. On the distribution of orbits of geometrically finite hyperbolic groups on the boundary
    (with Seonhee Lim) Ergod. Th. & Dynam. Sys., Vol 32, 173–189 (2012) (pdf)
  9. Almost prime Pythagorean triples in Thin orbits
    (with Alex Kontorovich) J. Reine Angew. Math. Vol 667 (2012), 89–131 (pdf)
  10. Effective equidistribution of $S$-integral points on symmetric varieties
    (with Yves Benoist) Annales de L'Institut Fourier, Vol 62 (2012), 1889–1942 (pdf )
  11. Apollonian circle packings and closed horospheres on hyperbolic 3 manifolds
    (with Alex Kontorovich, and an appendix by Oh and Shah) Journal of AMS. 24 (2011), 603–648 (pdf)
  12. Rational points on homogeneous varieties and Equidistribution of Adelic periods
    (with Alex Gorodnik, and with an appendix by Mikhail Borovoi) GAFA, Vol 21 (2011), 319–392 (pdf)
  13. 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)
  14. Discreteness criterion for subgroups of products of SL(2)
    (with Yves Benoist) Transformation Groups, Vol 15 (2010), 503–515 (pdf)
  15. Orbital counting via mixing and unipotent flows
    in Homogeneous flows, Moduli Spaces and Arithmetic, Clay Mathematics Proceedings, 2010, Vol 10, 339–375 (pdf)
  16. Strong Wavefront lemma and counting lattice points in sectors
    (with Alex Gorodnik and Nimish Shah) Israel J. Math., Vol 176 (2010), 419–444 (pdf)
  17. Discrete subgroups of SL_3(R) generated by triangular matrices
    (with Yves Benoist) Int. Math. Res. Notices, Article ID 149, 2009 (pdf)
  18. Integral points on symmetric varieties and Satake compactifications
    (with Alex Gorodnik and Nimish Shah). American J. Math., Vol 131 (2009), 1–57 (pdf)
  19. Manin's and Peyre's conjectures on rational points and Adelic mixing
    (with Alex Gorodnik and Francois Maucourant) Ann. Sci. Ecole Norm. Sup. Vol 41 (2008) 47–97 (pdf)

  20. Polar decomposition for p-adic symmetric spaces
    (with Yves Benoist) Int. Math. Res. Notices (2007), Article ID 121 (pdf)
  21. Equidistribution of rational matrices in their conjugacy classes
    (with Yves Benoist) Geom. and Funct. Analysis, Vol 17 (2007) (pdf)
  22. Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
    (with Alex Gorodnik) Duke Math. J. Vol 139 (2007), 483–525 (pdf)
  23. Representations of integers by an invariant polynomial and unipotent flows
    (with Alex Eskin) Duke Math. J., Vol 135 (2006), 481–506 (pdf)
  24. Ergodic theoretic proof of equidistribution of Hecke points
    (with Alex Eskin) Erg. The & Dyn. Sys, Vol 26 (2006), 163–167 (pdf)
  25. On uniform exponential growth for linear groups
    (with Alex Eskin and Shahar Mozes) Inventiones Math. Vol 160 (2005), 1–30 (pdf)
  26. Lattice action on finite volume homogeneous spaces
    J. Korean Math. Soc., Vol 42 (2005), 635–653 (pdf)
  27. 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)
  28. On a problem concerning arithmeticity of discrete groups acting on $H \times ... \times H$
    in "Algebraic groups and Arithmetic" (TIFR, India) (pdf)
  29. Harmonic analysis and Hecke operators
    in "Rigidity in Dynamics and Geometry", Springer-Verlag, edited by Burger and Iozzi (pdf)
  30. Hardy-Littlewood system and representations of integers by an invariant polynomial
    Geom. and Funct. Analysis, Vol 14 (2004) 791–809 (pdf)
  31. Finiteness of compact maximal flats of bounded volume
    Ergod. Th and Dynam. Sys. Vol 24 (2004), 217–225 (pdf)
  32. Cartan decomposition subgroups of SO(2,n)
    (with Dave Witte) Trans. AMS Vol 356 (2004) 1–38 (pdf)
  33. Equidistribution of integer points on a family of homogeneous varieties: a problem of Linnik
    (with Wee Teck Gan) Compositio Math. Vol 136 (2003), 323–352 (pdf)
  34. Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
    Duke Math. J., vol 113 (2002), pp. 133–192 (pdf)
  35. Uniform exponential growth for linear groups (announcement)
    (with Alex Eskin and Shahar Mozes) Int. Math. Res. Not. no 31 (2002), 1675–1683
  36. Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
    (with Dave Witte) Geom. Dedicata, vol 89 (2002), 25–57 (pdf)
  37. Hecke operators and equidistribution of Hecke points
    (with Laurant Clozel and Emmanuel Ullmo) Inventiones Math., vol 144 (2001), pp. 327–351 (pdf)
  38. Adelic version of Margulis arithmeticity theorem
    Math. Ann. vol 321 (2001), 4, pp. 789–815 (pdf)
  39. 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)
  40. S-arithmeticity of discrete subgroups containing lattices in horospherical subgroups
    Duke Math. J., vol 101 (2000), pp. 209–219
  41. On discrete subgroups containing a lattice in a horospherical subgroup
    Israel J. of Math., vol 110 (1999), pp. 333–340 (pdf)
  42. Tempered subgroups and representations with minimal decay of matrix coefficients
    Bull. Math. Soc. France, vol 126 (1998), pp. 355–380 (pdf) Minor correction: (pdf)
  43. Discrete subgroups generated by lattices in opposite horospherical subgroups
    J. Algebra, vol 203 (1998), pp. 621–676 (pdf)
  44. Arithmetic properties of some Zariski dense subgroups
    Proceedings of International Colloquium on "Lie groups and Ergodic theory" in TIFR, Bombay, 1996
  45. 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)