There is no fear in love.
But perfect love drives out fear,
because fear has to do with punishment.
The one who fears is not made perfect in love.

---1 John 4:18

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

Photo with Yoon-young

Photo with Pythagoras

Seminars

Other Brown seminars

Lecture Notes

2004 Winter: Group actions on homogeneous spaces (ps or pdf )

Slides of talks

Diophantine problems and group actions
(AMS 2005, Spring Central Section Meeting, Plenary lecture, April 9) (pdf)

Orbits of lattices on a symmetric space and the Furstenberg boundary
(talk given at Maryland-Pennstate Workshop on Dynamical Systems and Related topics conference, March 2005) (pdf)

Some preprints and publications

• Rational points on homogeneous varieties and Equidistribution of Adelic periods .
  (with A. Gorodnik, and with an appendix by M. Borovoi) As of April 1, 2008. (pdf or ps)

• Effective equidistribution of $S$-integral points on symmetric varieties .
  (with Y. Benoist). updated version as of Oct 2007 (pdf or ps)

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

• Strong Wavefront lemma and counting lattice points in sectors .
  (with A. Gorodnik and N. Shah). (pdf or ps)

• Integral points on symmetric varieties and Satake compactifications .
  (with A. Gorodnik and N. Shah). To appear in American J. Math (pdf or ps)

• Manin's and Peyre's conjectures on rational points and Adelic mixing .
  (with A. Gorodnik and F. Maucourant). To appear in Ann. Sci. Ecole Norm. Sup. (pdf or ps)

• Equidistribution of rational matrices in their conjugacy classes .
  (with Y. Benoist). GAFA., Vol 17 (2007) (pdf or ps)

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

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

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

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

• 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 or ps)

• Hardy-Littlewood system and representations of integers by an invariant polynomial .
  GAFA, Vol 14 (4), (2004) 791--809 (pdf or ps) Minor correction: (ps)

• Finiteness of compact maximal flats of bounded volume .
  Ergod. Th and Dynam. Sys. Vol 24(1), (2004), 217--225 (pdf or ps)

• On uniform exponential growth for linear groups .
  (with A. Eskin and S. Mozes). Invent. Math. Vol 160 (1), (2005), 1--30 (dvi or ps)

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

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

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

• Equidistribution of integer points on a family of homogeneous varieties: a problem of Linnik.
  (with W. T. Gan). Compositio Math. Vol 136 (2003), 323--352 (dvi or ps)

• Hecke operators and equidistribution of Hecke points .
  (with L. Clozel and E. Ullmo). Invent. Math., vol 144 (2001), pp. 327-351 (dvi or ps)

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

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

• New examples of compact Clifford-Klein forms of homogeneous spaces of SO(2,n) .
  (with D. Witte). IMRN, 2000, no 5, pp. 235-251

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

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

• 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

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

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

• 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