Nimish A. SHAH

Professor, Department of Mathematics

The Ohio State University, Columbus, Ohio 43210.

Email: shah AT math.osu.edu

Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics. (With Rodolphe Richard)

23 pages. arXiv:1305.6557

Equidistribution of primitive rational points on expanding horospheres. (latest) (With M. Einsiedler, S. Mozes, and U. Shapira)

To
appear in *Compositio*** Mathematica**, 33 pages. arXiv:1305.2678

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

Counting visible circles on the sphere and Kleinian groups (With H. Oh).

To appear in *Proceedings
of the conference on `Geometry,
Topology, and Dynamics in Negative Curvature*

(An ICM 2010
Satellite conference, Bangalore, India) to be published by the **LMS Lecture notes series**.

16 pages. *arXiv:1004.2129*

Equidistribution and Counting for orbits of geometrically finite hyperbolic groups(With H. Oh).

* J. Amer. Math. Soc. (JAMS)*, 26 (2013), 511 – 562. 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 2010**, Hyderabad,
India.

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)/Γ's.

*Seminaires** et Congres** 20
(2009),
71-106.*

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. *