Nimish A.
SHAH
Professor,
Department of Mathematics
The
Ohio State University, Columbus, Ohio 43210.
Email:
shah AT math.osu.edu
List
of Papers:
Quantitative behavior of unipotent
flows and an effective avoidance principle. (With Elon Lindenstrauss, Amir Mohammadi, Gregory Margulis). 52 pages. arXiv:1904.00290.
Primitive
rational points and higher powers on expanding horocycles in the modular
surface.(With Manfred Einsiedler and Manuel Luethi).
Ergodic Theory and Dynamical Systems,
1-45. doi:10.1017/etds.2020.15. arXiv:1901.03078
Expanding translates of shrinking
submanifolds in homogeneous spaces and Diophantine approximation.(With
Pengyu Yang). 16 pages. arXiv:1809.05570
Equidistribution of dilated curves on
nilmanifolds.(With Bryna Kra and Wenbo Sun).
J. Lond. Math. Soc. (2) 98 (2018), no. 3, 708--732. DOI:10.1112/jlms.12156
Equidistribution
of curves in homogeneous spaces and Dirichlet's approximation theorem for
matrices. (With Lei Yang).
Discrete
and Continuous Dynamical Systems-A, 40(2020), no. 9, 5247-5287. DOI: 10.3934/dcds.2020227
arXiv:1606.00152
Geometric results on linear actions of
reductive Lie groups for applications to homogeneous dynamics.(With
Rodolphe Richard) Ergodic
Theory Dynamical Systems,
38 (2018), no. 7, 2780--2800. DOI:10.1017/etds.2016.138
Equidistribution
of primitive rational points on expanding horospheres.(With M. Einsiedler,
S. Mozes, and U. Shapira) Compositio Mathematica, 152
(2016), 667 - 692. DOI:10.1112/S0010437X15007605.
Counting visible circles
on the sphere and Kleinian groups. (With H. Oh).
In: Geometry, topology, and
dynamics in negative curvature, London Math. Soc. Lecture Note Ser.,
425, Cambridge
Univ. Press, Cambridge, 2016. DOI:10.1017/CBO9781316275849.009
Limits of translates of
divergent geodesics and Integral points on one-sheeted hyperboloids. (With
H. Oh).
Israel J. Math., 199 (2014), no. 2, 915-931. DOI: 10.1007/s11856-013-0063-2
Equidistribution and
Counting for orbits of geometrically finite hyperbolic groups. (With H. Oh).
J. Amer. Math. Soc. (JAMS), 26 (2013), 511 Р562. DOI:
10.1090/S0894-0347-2012-00749-8
The Asymptotic
distribution of circles in the orbits of Kleinian groups. (With H. Oh).
Inventiones Math., 187 (2012), no. 1, 1-35. DOI: 10.1007/s00222-011-0326-7.
Equidistribution of
translated curves on homogeneous spaces and Dirichlet's approximation.
Proceedings of the
International Congress of Mathematicians, Volume
III, 1332--1343, Hindustan Book
Agency, New Delhi, 2010.
Khinchin theorem for integral points on quadratic varieties.
(With A. Gorodnik).
Math. Annalen, 350 (2011), no. 2, 357-380. DOI:
10.1007/s00208-010-0561-z.
Expanding translates
of curves and Dirichlet-Minkowski theorem on linear forms.
J. Amer. Math. Soc. (JAMS), 23
(2010), 563-589.
Strong wave
front lemma and counting integral points in sectors of symmetric varieties. (With H. Oh and A. Gorodnik).
Israel J. Math., 176 (2010),
419-443.
Inventiones Math., 177
(2009), 509-532.
Limiting
distributions of evolution of smooth curves under geodesic flow on hyperbolic
manifolds.
Duke Math. J., 148
(2009), no. 2, 281-304.
Limiting distributions
of curves under geodesic flow on hyperbolic manifold.
Duke Math J., 148
(2009), 251-279.
Unipotent flows on
products of SL(2,K)/
's.
Dynamical
systems and Diophantine approximation, 69--104, Séminaires et Congrès, 19, Soc.
Math. France, Paris, 2009.
Integral points on symmetric
varieties and Satake compactifications. (With H. Oh and A. Gorodnik).
Amer. J. Math., 131
(2009), no. 1, 1-57.
Locally compact
groups with dense orbits under $Z^d$-actions by
automorphisms. (With S.G.
Dani and G.A. Willis).
Ergodic Theory Dynam. Systems, 26
(2006), no. 5, 1443--1465.
Dynamics of subgroup
actions on homogeneous spaces of Lie groups and applications to number theory.(With
D. Kleinbock and A. Starkov).
Handbook of dynamical systems (ed. A. Katok and B. Hasselblatt), Vol.
1A, Chapter 11, 813--930, North-Holland, Amsterdam, 2002.
Counting integral
matrices with a given characteristic polynomial.
Sankhya (Ser. A), 62 (2000), no. 3, 386--412.
On actions of
epimorphic subgroups on homogeneous spaces. (With Barak Weiss).
Ergodic Theory Dynam. Systems, 20
(2000), no. 2, 567-59.
Lie groups and ergodic theory.
Proceedings of the
International Colloquium held in Mumbai, Jan 4-12, 1996.
Tata Inst. Fund.Res.
Stud. Math., 14, Tata Inst. Fund.
Res., Bombay, 1998.
Correction to
"Unipotent flows and counting lattice points on homogeneous
varieties".(With A. Eskin and S. Mozes). 2 pages, May 1998.
Unipotent flows and counting
lattice points on homogeneous varieties.
Annals of Math., 143 (1996), no. 2, 253--299.
Non-divergence of
translates of certain algebraic measures. (With A. Eskin and S.
Mozes).
Geom. Funct. Anal. (GAFA), 7 (1997), no. 1,
48-80.
Limit
distributions of expanding translate of certain orbits on homogeneous spaces.
Proc. Indian Acad. Sci. Math. Sci., 106 (1996), no. 2,
105--125.
On the space of
ergodic invariant measures of unipotent flows. (With S. Mozes).
Ergodic Theory Dynam. Systems, 15
(1995), no. 1, 149--159.
Limit distributions of
polynomial trajectories on homogeneous spaces.
Duke Math. J., 75
(1994), no. 3, 711--732.
Closures of totally
geodesic immersions in manifolds of constant negative curvature.
Group theory from a geometrical
viewpoint (Trieste, 1990), 718--732, World Sci. Publ., River Edge,
NJ, 1991.
Uniformly distributed
orbits of certain flows on homogeneous spaces.
Math. Annalen, 289
(1991), no. 2, 315--334.
DISSERTATIONS:
Unipotent flows on
homogeneous spaces. Ph.D. Thesis, Tata Institute of Fundamental
Research, Mumbai, 1994.
Unipotent flows on
homogeneous spaces of SL(2,C). M.Sc. Thesis, Tata Institute of
Fundamental Research, Mumbai, 1992.