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 Dirichlet’s 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.