
Rigidity of Kleinian groups via selfjoinings II: measure theoretic version.
(with D. Kim), Preprint (pdf, Last part of video)

Conformal measure preserving representations and selfjoinings.
(with D. Kim), Preprint (pdf, Last part of video)

Rigidity of Kleinian groups via selfjoinings.
(with D. Kim), Preprint (arXiv:2208.05806) (pdf, video)

Torus counting and selfjoinings of Kleinian groups.
(with S. Edwards and M. Lee), Preprint (arXiv:2210.10229) (pdf)

Euclidean traveller in hyperbolic worlds.
Notices Amer. Math. Soc. 69 (2022), no. 11, 18881897 (pdf , video)

Dichotomy and measures on limit sets of Anosov groups.
(with M. Lee), Preprint (arXiv:2203.06794) (pdf)

Temperedness of L^2(\Gamma\G) and positive eigenfunctions
in higher rank.
(with S. Edwards), Preprint (arXiv:2202.06203) (pdf)

On denseness of horospheres in
higher rank homogeneous spaces.
(with O. Landesberg), Preprint (arXiv:2202.05044) (pdf)

Hausdorff dimension of directional limit sets
for selfjoinings
of hyperbolic manifolds.
(with D. Kim and Y. Minsky), Preprint (pdf)

Tent property of the growth indicator functions and applications.
(with D. Kim and Y. Minsky), Preprint (pdf)

Uniqueness of conformal measures and local mixng for Anosov groups.
(with S. Edwards and M. Lee), Michigan Math. J. 72 (Prasad volume), 243259 (pdf)

Horospherical invariant measures and a rank dichotomy for Anosov groups.
(with O. Landesberg, M. Lee, and E. Lindenstrauss), Preprint (arXiv:2106.02635), To appear in Journal of Modern Dynamics (pdf, video)

The HopfTsujiSullivan dichotomy in higher rank and applications to Anosov subgroups.
(with M. Burger, O. Landesberg, and M. Lee), Preprint (arXiv:2105.13930), To appear in Journal of Modern Dynamics (pdf, video)

Ergodic decompositions of geometric measures on Anosov homogeneous spaces.
(with M. Lee), To appear in Israel J. Math (arXiv:2010.11337) (pdf, video)

Invariant measures for
horospherical actions and Anosov groups.
(with M. Lee), To appear in Int. Math. Res. Notices (arXiv:
2008.05296) (pdf, video part 1, video part 2)

Anosov groups: local mixing, counting, and equidistribution.
(with S. Edwards and M. Lee), To appear in Geometry & Topology, arXiv:2003.14277 (pdf)

Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds.
(with S. Edwards),
Duke Math. J, Vol 170 (2021), 34173458 (pdf)

Isolations of geodesic planes in the frame bundle of a
hyperbolic 3manifold.
(with A. Mohammadi), Preprint (arXiv:2002.06579), To appear in Compositio Math. (pdf)

Dynamics for discrete subgroups of SL(2,C).
In: Dynamics, Geometry, Number theory: The impact of Margulis on Modern Mathematics (pdf)

Topological proof of BenoistQuint's orbit closure theorem for SO(d,1).
(with M. Lee),
Journal of Modern Dynamics, Vol 15 (2019), 263276 (pdf)

Orbit closures of unipotent flows for hyperbolic manifolds
with Fuchsian ends.
(with M. Lee), Preprint
(arXiv:1902.06621) (pdf, video).

Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds.
(with D. Kelmer),
Journal of Modern Dynamics, Vol 17 (2021), 401434 (pdf)

Orbit closures for the PSL(2,R)action on hyperbolic 3manifolds.
(Fields Institute Summer School Lecture Notes), Preprint (pdf)

Geodesic planes in geometrically finite
acylindrical 3manifolds.
(with Y. Benoist), Ergodic Theory and Dynamical Systems, Vol 42 (2022), 514553 (memorial volume for Katok) (pdf, video)

Geodesic planes in the convex core of an
acylindrical 3manifold.
(with C. McMullen and A. Mohammadi), Duke. Math. J, 171 (2022), no. 5, 10291060.
(pdf, video )

Local mixing and invariant measures for
horospherical subgroups on abelian covers.
(with W. Pan), IMRN 2019, Issue 19, 60366088
(pdf)

Remembering Marina Ratner.
AMS Notices Amer. Math. Soc. 66 (2019), No. 3, p. 385
(pdf)

Prime number theorems and
holonomies for hyperbolic rational maps.
(with D. Winter), Inventiones Mathematicae, Vol 208 (2017), 401440
(pdf, video)

Horocycles in hyperbolic 3manifolds.
(with C. McMullen and A. Mohammadi), Geometric and Functional Analsis, Vol 26 (2016), 961973
(pdf)

Geodesic planes in hyperbolic 3manifolds.
(with C. McMullen and A. Mohammadi), Inventiones Mathematicae, Vol 209 (2017), 425461
(pdf, video)

Invariant Radon measures for unipotent flows and
products of Kleinian groups.
(with A. Mohammadi), PAMS. 146 (2018), 14691479
(pdf)

Fuchsian groups and compact hyperbolic surfaces.
(with Y. Benoist), L'Enseignement MathÃ©matique, Vol 62 (2016), 189198
(pdf)

Uniform congruence counting for Schottky semigroups in SL_2(Z).
(with M. Magee and D. Winter),
J. Reine Angew. Math., Vol 753 (2019), 89135
(pdf)

Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z).
(with D. Winter), Journal of the American Mathematical Society, Vol 29 (2016), 10691115
(pdf)

Closed geodesics and holonomies for Kleinian manifolds.
(with G. Margulis and A. Mohammadi),
Geometric and Functional analysis, Vol 24 (2014), 16081636
(pdf, video)

Classification of joinings for Kleinian groups.
(with A. Mohammadi), Duke Math.J., Vol 165 (2016), 21552223
(pdf, video)

Matrix coefficients, counting and primes for orbits of geometrically finite groups.
(with A. Mohammadi), Journal of the
European Mathematical Society, Vol 17 (2015), 837897
(pdf)

Ergodicity of unipotent flows and Kleinian groups.
(with A. Mohammadi),
Journal of the American Mathematical Society, Vol 28 (2015), 531577
(pdf, video)

Eigenvalues of congruence covers of geometrically finite hyperbolic manifolds.
Journal of Geometric
Analysis, Vol 25 (2015), 14211430 (pdf)

Counting visible circles on the sphere and Kleinian groups.
(with N. Shah), LMS series Vol 425, 272288.
(pdf)

Apollonian circle packings: dynamics and number theory.
Japanese Journal of Math., Vol 9 (2014), 6997,
(expanded version of the 13th Takagi Lecture series notes).
(pdf)

Harmonic analysis, ergodic theory and counting for
thin groups.
In "Thin groups and superstrong approximation", MSRI publ.61
Cambridge Univ. Press. 2014
(pdf)

Limits of translates of divergent geodesics and integral points on onesheeted hyperboloids.
(with N. Shah), Israel J. Math., Vol 199 (2014),
pp. 915931
(pdf)

Effective circle count for Apollonian packings and
closed horospheres.
(with M. Lee),
Geometric and Functional analysis, Vol 23 (2013), 580621
(pdf)

Equidistribution and counting for orbits of geometrically
finite hyperbolic groups.
(with N. Shah),
Journal of the American Mathematical Society, Vol 26 (2013), 511562
(pdf)

The asymptotic distribution of circles in the orbits of
Kleinian groups.
(with N. Shah),
Inventiones Mathematicae, Vol 187 (2012), 135
(pdf)

On the distribution of orbits of geometrically finite hyperbolic groups on the boundary.
(with S. Lim), Ergod. Th. & Dynam. Sys.,
Vol 32, 173189 (2012)
(pdf)

Almost prime Pythagorean triples in thin orbits.
(with A. Kontorovich), J. Reine Angew. Math.
Vol 667 (2012), 89131
(pdf)

Effective equidistribution of Sintegral points on symmetric varieties.
(with Y. Benoist),
Annales de L'Institut Fourier, Vol 62 (2012), 18891942
(pdf )

Apollonian circle packings and closed horospheres on
hyperbolic 3 manifolds.
(with A. Kontorovich),
Journal of the American Mathematical Society 24 (2011), 603648
(pdf)

Rational points on homogeneous varieties and equidistribution of adelic periods.
(with A. Gorodnik),
Geometric and Functional Analysis, Vol 21 (2011), 319392
(pdf)

Dynamics on geometrically finite hyperbolic manifolds with
applications to Apollonian circle packings and beyond.
Proceedings of International Congress of Mathematicians (2010),
Vol III, 13081331
(pdf)

Discreteness criterion for subgroups of products of SL(2).
(with Y. Benoist),
Transformation Groups, Vol 15 (2010), 503515
(pdf)

Orbital counting via mixing and unipotent flows.
in Homogeneous flows, Moduli Spaces and Arithmetic,
Clay Mathematics Proceedings, 2010, Vol 10, 339375
(pdf)

Strong wavefront lemma and counting lattice points in sectors.
(with A. Gorodnik and N. Shah),
Israel J. Math., Vol 176 (2010), 419444
(pdf)

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

Integral points on symmetric varieties and Satake
compactifications.
(with A. Gorodnik and N. Shah), American J. Math.,
Vol 131 (2009), 157
(pdf)

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) 4797
(pdf)

Polar decomposition for padic symmetric spaces.
(with Y. Benoist), Int. Math. Res. Notices (2007),
Article ID 121
(pdf)

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

Orbits of discrete subgroups on a symmetric space
and the Furstenberg boundary.
(with A. Gorodnik),
Duke Math. J. Vol 139 (2007), 483525
(pdf)

Representations of integers by an invariant polynomial and unipotent flows.
(with A. Eskin),
Duke Math. J., Vol 135 (2006), 481506
(pdf)

Ergodic theoretic proof of equidistribution of Hecke points.
(with A. Eskin),
Erg. The & Dyn. Sys, Vol 26 (2006), 163167
(pdf)

On uniform exponential growth for linear groups.
(with A. Eskin and S. Mozes),
Inventiones Math. Vol 160 (2005), 130
(pdf)

Lattice action on finite volume homogeneous
spaces.
J. Korean Math. Soc., Vol 42 (2005), 635653
(pdf)

The Ruziewicz problem and distributing points on
homogeneous spaces of a compact Lie group.
Israel J. Math (Furstenberg volume),
Vol 149 (2005), 301316
(pdf)

On a problem concerning arithmeticity of
discrete groups acting on H...H.
In "Algebraic groups and Arithmetic" (TIFR, India)
(pdf)

Harmonic analysis and Hecke operators.
In "Rigidity in Dynamics and Geometry", SpringerVerlag,
edited by Burger and Iozzi
(pdf)

HardyLittlewood system and representations of integers by
an invariant polynomial.
Geom. and Funct. Analysis, Vol 14 (2004) 791809
(pdf)

Finiteness of compact maximal flats of bounded volume.
Ergod. Th and Dynam. Sys. Vol 24 (2004), 217225
(pdf)

Cartan decomposition subgroups of SO(2,n).
(with D. Witte), Trans. AMS Vol 356 (2004) 138
(pdf)

Equidistribution of integer points on a family of
homogeneous varieties: a problem of Linnik.
(with W. Gan), Compositio Math. Vol 136 (2003), 323352
(pdf)

Uniform pointwise bounds for matrix coefficients of unitary
representations and applications to Kazhdan constants.
Duke Math. J., vol 113 (2002), pp. 133192
(pdf)

Uniform exponential growth for linear groups. (announcement)
(with A. Eskin and S. Mozes) Int. Math. Res. Not. no 31 (2002), 16751683

Compact CliffordKlein forms of homogeneous spaces of SO(2,n).
(with D. Witte), Geom. Dedicata, vol 89 (2002), 25–57
(pdf)

Hecke operators and equidistribution of Hecke points.
(with L. Clozel and E. Ullmo), Inventiones Math.,
vol 144 (2001), pp. 327351
(pdf)

Adelic version of Margulis arithmeticity theorem.
Math. Ann. vol 321 (2001), 4, pp. 789815
(pdf)

New examples of compact CliffordKlein forms of homogeneous
spaces of SO(2,n).
(with Dave Witte), IMRN, 2000, no 5, pp. 235251
(pdf)

Sarithmeticity of discrete subgroups containing lattices in
horospherical subgroups.
Duke Math. J., vol 101 (2000), pp. 209219

On discrete subgroups containing a lattice in a
horospherical subgroup.
Israel J. of Math., vol 110 (1999), pp. 333340
(pdf)

Tempered subgroups and representations with minimal decay of matrix coefficients.
Bull. Math. Soc. France, vol 126 (1998), pp. 355380
(pdf)
Minor correction: (pdf)

Discrete subgroups generated by lattices in opposite horospherical subgroups.
J. Algebra, vol 203 (1998), pp. 621676
(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. 12191224
(pdf)