Nimish A. Shah

Professor, Department of Mathematics

The Ohio State University, Columbus, Ohio 43210

Email: shah.595@osu.edu

ORCID: 0000-0002-6459-6208

Department profile · arXiv papers

Publications and preprints

  1. Birkhoff genericity on affine subspaces in horospheres. With Pengyu Yang. 37 pages (June 2026). arXiv
  2. Limit distributions for SO(n,1) actions on k-lattices in ℝn+1. With Michael Bersudsky. Transactions of the American Mathematical Society (2026). PDFDOI
  3. An effective closing lemma for unipotent flows. With Elon Lindenstrauss, Gregory Margulis, Amir Mohammadi, and Andreas Wieser. 24 pages (October 2024). To appear in Journal d’Analyse Mathématique. DOI
  4. Equidistribution of polynomially bounded o-minimal curves in homogeneous spaces. With Michael Bersudsky and Hao Xing. Duke Mathematical Journal 175, no. 3 (2026), 437–510. arXivDOI
  5. An upper bound of the Hausdorff dimension of singular vectors on affine subspaces. With Pengyu Yang. Transactions of the American Mathematical Society, Series B 11 (2024), 1249–1265. arXivDOI
  6. Equidistribution of non-uniformly stretching translates of shrinking smooth curves and weighted Dirichlet approximation. With Pengyu Yang. Mathematische Zeitschrift 308, article 60 (2024). arXiv
  7. Equidistribution of expanding degenerate manifolds in the space of lattices. With Pengyu Yang. Proceedings of the London Mathematical Society 129, no. 4 (2024), e12634. DOI
  8. Equidistribution in the space of 3-lattices and Dirichlet-improvable vectors on planar lines. With Dmitry Kleinbock, Nicolas de Saxcé, and Pengyu Yang. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 25, no. 1 (2024), 565–604. arXivDOI
  9. Quantitative behavior of unipotent flows and an effective avoidance principle. With Elon Lindenstrauss, Gregory Margulis, and Amir Mohammadi. Journal d’Analyse Mathématique 153 (2024), 1–61. DOI
  10. Expanding translates of shrinking submanifolds in homogeneous spaces and Diophantine approximation. With Pengyu Yang. Journal of Modern Dynamics 19 (2023), 947–965. arXiv
  11. Primitive rational points on expanding horocycles in products of the modular surface with the torus. With Manfred Einsiedler and Manuel Lüthi. Ergodic Theory and Dynamical Systems 41, no. 6 (2021), 1706–1750. arXivDOI
  12. Equidistribution of curves in homogeneous spaces and Dirichlet’s approximation theorem for matrices. With Lei Yang. Discrete and Continuous Dynamical Systems—A 40, no. 9 (2020), 5247–5287. arXivDOI
  13. Equidistribution of dilated curves on nilmanifolds. With Bryna Kra and Wenbo Sun. Journal of the London Mathematical Society (2) 98, no. 3 (2018), 708–732. DOI
  14. Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics. With Rodolphe Richard. Ergodic Theory and Dynamical Systems 38, no. 7 (2018), 2780–2800. DOI
  15. Equidistribution of primitive rational points on expanding horospheres. With Manfred Einsiedler, Shahar Mozes, and Uri Shapira. Compositio Mathematica 152 (2016), 667–692. arXivDOI
  16. Counting visible circles on the sphere and Kleinian groups. With Hee Oh. In Geometry, Topology, and Dynamics in Negative Curvature, London Mathematical Society Lecture Note Series 425 (Cambridge University Press, 2016), 272–288. arXivDOI
  17. Limits of translates of divergent geodesics and integral points on one-sheeted hyperboloids. With Hee Oh. Israel Journal of Mathematics 199, no. 2 (2014), 915–931. arXivDOI
  18. Equidistribution and counting for orbits of geometrically finite hyperbolic groups. With Hee Oh. Journal of the American Mathematical Society 26 (2013), 511–562. arXivDOI
  19. The asymptotic distribution of circles in the orbits of Kleinian groups. With Hee Oh. Inventiones Mathematicae 187, no. 1 (2012), 1–35. arXivDOI
  20. Equidistribution of translated curves on homogeneous spaces and Dirichlet’s approximation. In Proceedings of the International Congress of Mathematicians 2010, vol. 3, 1332–1343 (Hindustan Book Agency, 2010). ProceedingsVolume 3
  21. Khinchin theorem for integral points on quadratic varieties. With Alexander Gorodnik. Mathematische Annalen 350, no. 2 (2011), 357–380. arXivDOI
  22. Expanding translates of curves and Dirichlet–Minkowski theorem on linear forms. Journal of the American Mathematical Society 23 (2010), 563–589. arXivDOI
  23. Strong wave front lemma and counting integral points in sectors of symmetric varieties. With Hee Oh and Alexander Gorodnik. Israel Journal of Mathematics 176 (2010), 419–443. arXivDOI
  24. Equidistribution of expanding translates of curves and Dirichlet’s theorem on Diophantine approximation. Inventiones Mathematicae 177 (2009), 509–532. arXivDOI
  25. Limiting distributions of evolution of smooth curves under geodesic flow on hyperbolic manifolds. Duke Mathematical Journal 148, no. 2 (2009), 281–304. arXivDOI
  26. Limiting distributions of curves under geodesic flow on hyperbolic manifolds. Duke Mathematical Journal 148, no. 2 (2009), 251–279. arXivDOI
  27. Unipotent flows on products of SL(2,K)/Γ. In Dynamical Systems and Diophantine Approximation, Séminaires et Congrès 19 (Société Mathématique de France, 2009), 69–104. arXivPublisher
  28. Integral points on symmetric varieties and Satake compactifications. With Hee Oh and Alexander Gorodnik. American Journal of Mathematics 131, no. 1 (2009), 1–57. arXivJSTOR
  29. Locally compact groups with dense orbits under ℤd-actions by automorphisms. With S. G. Dani and G. A. Willis. Ergodic Theory and Dynamical Systems 26, no. 5 (2006), 1443–1465. DOI
  30. Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory. With Dmitry Kleinbock and Alexander Starkov. In Handbook of Dynamical Systems, vol. 1A (Elsevier, 2002). DOI
  31. Counting integral matrices with a given characteristic polynomial. Sankhyā, Series A 62, no. 3 (2000), 386–412. arXivJSTOR
  32. On actions of epimorphic subgroups on homogeneous spaces. With Barak Weiss. Ergodic Theory and Dynamical Systems 20, no. 2 (2000), 567–592. DOI
  33. Invariant measures and orbit closures on homogeneous spaces for actions of subgroups generated by unipotent elements. In Lie Groups and Ergodic Theory, Tata Institute of Fundamental Research Studies in Mathematics 14 (1998), 229–271. Book
  34. Unipotent flows and counting lattice points on homogeneous varieties. Annals of Mathematics 143, no. 2 (1996), 253–299. DOI

    Correction, with Alex Eskin and Shahar Mozes (May 1998), 2 pages.

  35. Non-divergence of translates of certain algebraic measures. With Alex Eskin and Shahar Mozes. Geometric and Functional Analysis 7, no. 1 (1997), 48–80. DOI
  36. Limit distributions of expanding translates of certain orbits on homogeneous spaces. Proceedings of the Indian Academy of Sciences—Mathematical Sciences 106, no. 2 (1996), 105–125. arXivDOI
  37. On the space of ergodic invariant measures of unipotent flows. With Shahar Mozes. Ergodic Theory and Dynamical Systems 15, no. 1 (1995), 149–159. DOI
  38. Limit distributions of polynomial trajectories on homogeneous spaces. Duke Mathematical Journal 75, no. 3 (1994), 711–732. DOI
  39. Closures of totally geodesic immersions in manifolds of constant negative curvature. In Group Theory from a Geometrical Viewpoint (Trieste, 1990), 718–732 (World Scientific, 1991). Book DOI
  40. Uniformly distributed orbits of certain flows on homogeneous spaces. Mathematische Annalen 289, no. 2 (1991), 315–334. DOI

Dissertations

  1. Unipotent flows on homogeneous spaces. Ph.D. thesis, Tata Institute of Fundamental Research, Mumbai, 1994. 69 pages.
  2. Unipotent flows on homogeneous spaces of SL(2,ℂ). M.Sc. thesis, Tata Institute of Fundamental Research, Mumbai, 1992. 112 pages.