Blessed is the man
who does not walk in the councel of the wicked
or stand in the way of sinners
or sit in the seat of mockers.
But his delight is in the law of the LORD,
and on his law he meditates day and night.
He is like a tree planted by streams of water,
which yields its fruit in season
and whose leaf does not wither.

--from Psalm 1

How to reach me

• Paper mail:
  Box 1917
  151 Thayer Street
  Providence, RI 02912
  USA

• E-mail: heeoh(AT)math(DOT)brown(DOT)edu
  
• Phone: (401) 863-1134 (office)
  
• Fax: (401) 863-9013
  
• Office: 113 Kassar
  

Curriculum Vitae

Teaching

Seminars

In press

Slides

Preprints and publications

• Ergodicity of unipotent flows and geometrically finite Kleinian groups
  (with Amir Mohammadi) Preprint as of Dec 2011, Submitted (pdf)

• Effective circle count for Apollonian packings and closed horospheres
  (with Min Lee) Updated as of March 21, 2012, Submitted (the paper titled by "effective equidistribution of closed horocycles for geometrically finite surfaces" has been merged into this new version) (pdf)

• Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
  (with Nimish Shah), under revision for Journal of AMS (pdf)

• The asymptotic distribution of circles in the orbits of Kleinian groups
  (with Nimish Shah) Inventiones Mathematicae, Vol 187 (2012), 1--35 (pdf)

• 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)

• 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)

• 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)

• Limits of translates of divergent geodesics and integral points on one-sheeted hyperboloids
  (with Nimish Shah) Preprint, Submitted (pdf)

• Counting visible circles on the sphere and Kleinian groups
  (with Nimish Shah) Preprint (updated as of Nov, 2010), Submitted (pdf)

• Almost prime Pythagorean triples in Thin orbits
  (with Alex Kontorovich) To appear in Crelle's journal (pdf)

• Discreteness criterion for subgroups of products of SL(2)
  (with Yves Benoist) Transformation Groups, Vol 15 (2010), 503--515 (pdf)

• Orbital counting via mixing and unipotent flows
  in Homogeneous flows, Moduli Spaces and Arithemetic, Clay Mathematics Proceedings, 2010, Vol 10, 339--375 (pdf)

• 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)

• Effective equidistribution of $S$-integral points on symmetric varieties
  (with Yves Benoist) To appear in Annales de L'Institut Fourier (pdf )

• Strong Wavefront lemma and counting lattice points in sectors
  (with Alex Gorodnik and Nimish Shah) Israel J. Math., Vol 176 (2010), 419--444 (pdf)

• Discrete subgroups of SL_3(R) generated by triangular matrices
  (with Yves Benoist) Int. Math. Res. Notices, Article ID 149, 2009 (pdf)

• Integral points on symmetric varieties and Satake compactifications
  (with Alex Gorodnik and Nimish Shah). American J. Math., Vol 131 (2009), 1--57 (pdf)

• 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)

• Polar decomposition for p-adic symmetric spaces .
  (with Yves Benoist) Int. Math. Res. Notices (2007), Article ID 121 (pdf)

• Equidistribution of rational matrices in their conjugacy classes
  (with Yves Benoist) Geom. and Funct. Analysis, Vol 17 (2007) (pdf)

• Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
  (with Alex Gorodnik) Duke Math. J. Vol 139 (2007), 483--525 (pdf)

• Representations of integers by an invariant polynomial and unipotent flows
  (with Alex Eskin) Duke Math. J., Vol 135 (2006), 481--506 (pdf)

• Ergodic theoretic proof of equidistribution of Hecke points
  (with Alex Eskin) Erg. The & Dyn. Sys, Vol 26 (2006), 163--167 (pdf)

• On uniform exponential growth for linear groups
  (with Alex Eskin and Shahar Mozes) Inventiones Math. Vol 160 (2005), 1--30 (pdf)

• Lattice action on finite volume homogeneous spaces
  J. Korean Math. Soc., Vol 42 (2005), 635--653 (pdf)

• 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)

• On a problem concerning arithmeticity of discrete groups acting on $H \times ... \times H$
  in "Algebraic groups and Arithmetic" (TIFR, India) (pdf)

• Harmonic analysis and Hecke operators
  in "Rigidity in Dynamics and Geometry", Springer-Verlag, edited by Burger and Iozzi (pdf)

• Hardy-Littlewood system and representations of integers by an invariant polynomial
  Geom. and Funct. Analysis, Vol 14 (2004) 791--809 (pdf) Minor correction: (ps)

• Finiteness of compact maximal flats of bounded volume .
  Ergod. Th and Dynam. Sys. Vol 24 (2004), 217--225 (pdf)

• Cartan decomposition subgroups of SO(2,n)
  (with Dave Witte) Trans. AMS Vol 356 (2004) 1-38 (pdf)

• 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)

• Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
  Duke Math. J., vol 113 (2002), pp. 133-192 (pdf)

• Uniform exponential growth for linear groups (announcement) .
  (with Alex Eskin and Shahar Mozes) Int. Math. Res. Not. no 31 (2002), 1675-1683 (dvi or ps)

• Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
  (with Dave Witte) Geom. Dedicata, vol 89 (2002), 25-57 (pdf)

• Hecke operators and equidistribution of Hecke points
  (with Laurant Clozel and Emmanuel Ullmo) Inventiones Math., vol 144 (2001), pp. 327-351 (pdf)

• Adelic version of Margulis arithmeticity theorem
  Math. Ann. vol 321 (2001), 4, pp. 789-815 (pdf)

• 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)

• S-arithmeticity of discrete subgroups containing lattices in horospherical subgroups
  Duke Math. J., vol 101 (2000), pp. 209-219

• On discrete subgroups containing a lattice in a horospherical subgroup
  Israel J. of Math., vol 110 (1999), pp. 333-340 (pdf)

• Tempered subgroups and representations with minimal decay of matrix coefficients
  Bull. Math. Soc. France, vol 126 (1998), pp. 355-380 (pdf) Minor correction: (pdf)

• Discrete subgroups generated by lattices in opposite horospherical subgroups
  J. Algebra, vol 203 (1998), pp. 621-676 (pdf)

• Arithmetic properties of some Zariski dense subgroups
  Proceedings of International Colloquium on "Lie groups and Ergodic theory" in TIFR, Bombay, 1996

• 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 )