Nimish A. SHAH

Professor, Department of Mathematics

The Ohio State University, Columbus, Ohio 43210.

Email: shah AT

List of Papers:

    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.

Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation.

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.

Invariant measures and orbit closures on homogeneous spaces for actions of subgroups generated by unipotent elements.

             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.



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.