NIMISH A. SHAH

 

Tata Institute of Fundamental Research, Mumbai 400005, INDIA

 

 

LIST OF PAPERS:

 

 

        Khinchin theorem for integral points on quadratic varieties.

(With A. Gorodnik). 19 pages.

 

        Expanding translates of curves and Dirichlet-Minkowski theorem on linear forms.

Journal of the American Math Soc (JAMS). (To appear).

27 pages.

 

        Strong wave front lemma and counting integral points in sectors of symmetric†† varieties

(With H. Oh and A. Gorodnik).

Israel J. Math. (To appear). 22 pages.

 

        Equidistribution of expanding translates of curves and Dirichletís theorem on Diophantine approximation.

  Invent Math. 177 (2009), 509-532.

24 pages.

 

        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), no. 2, 251-279.

 

        Unipotent flows on products of SL(2,K)/Γ's.

Seminaires et congres, 22 (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, Vol. 1A, 813--930, North-Holland, Amsterdam, 2002.

 

        Counting integral matrices with a given characteristic polynomial.

Ergodic theory and harmonic analysis (Mumbai, 1999).

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 (Mumbai, 1996), 229--271,

Tata Inst. Fund. Res. Stud. Math., 14, Tata Inst. Fund. Res., Bombay, 1998. 

 

        Unipotent flows and counting lattice points on homogeneous varieties.

Annals of Math.(2) 143 (1996), no. 2, 253--299.

 

        Non-divergence of translates of certain algebraic measures

(With A. Eskin and S. Mozes).

Geom. Funct. Anal. 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. Ann. 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.