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
Expanding maps and Continued fractions
(with Michael Magee and Dale Winter).
(pdf)
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)
Classification of joinings for Kleinian groups
(with Amir Mohammadi) arXiv:1404.1510
(pdf)
Accepted for Publication
Ergodicity of unipotent flows and Kleinian groups
(with Amir Mohammadi) arXiv:1112.4024.
To appear in Journal of AMS.
(pdf)
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)
Eigenvalues of congruence covers of geometrically finite
hyperbolic manifolds
arXiv:1302.2950 To appear in Journal of Geometric
Analysis (pdf)
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
Closed geodesics and holonomies for Kleinian manifolds
(with Gregory Margulis and Amir Mohammadi)
GAFA, Vol 24 (2014), 1608–1636
(pdf)
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)
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)
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)
Effective circle count for Apollonian packings and
closed horospheres (with Min Lee),
GAFA, Vol 23 (2013), 580–621
(pdf)
Equidistribution and Counting for orbits of geometrically
finite hyperbolic groups (with Nimish Shah),
Journal of AMS, Vol 26 (2013), 511–562
(pdf)
The asymptotic distribution of circles in the orbits of
Kleinian groups (with Nimish Shah)
Inventiones Mathematicae, Vol 187 (2012), 1–35
(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)
Almost prime Pythagorean triples in Thin orbits
(with Alex Kontorovich) J. Reine Angew. Math.
Vol 667 (2012), 89–131
(pdf)
Effective equidistribution of $S$-integral points on
symmetric varieties (with Yves Benoist)
Annales de L'Institut Fourier, Vol 62 (2012), 1889–1942
(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)
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)
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)
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 Arithmetic,
Clay Mathematics Proceedings, 2010, Vol 10, 339–375
(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)
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
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)