Anish Ghosh

Current students: Shreyasi Datta, Prasuna Bandi, Mahbub Alam. Former students.

Current Postdocs: Debanjan Nandi, Gianluca Faraco.

Recent and Upcoming Events:Probabilistic methods in negative curvature 

                                                      Dynamical Systems - Summer School, EPFL 

                                                      Smooth and Homogeneous Dynamics

Publications

60) With Gaurav Aggarwal, Joint equidistribution of approximates, preprint 2024. 

59) With V. Beresnevich, S. Datta and B. Ward, Rectangular shrinking targets for Z^m actions on tori: well and badly approximable systems, https://arxiv.org/abs/2307.10122 .

58) With V. Beresnevich, S. Datta and B. Ward, Bad is Null, https://arxiv.org/abs/2307.10109 .

57) With Gaurav Aggarwal, Two Central limit theorems in Diophantine approximation, https://arxiv.org/abs/2306.02304 .

56) With Victor Beresnevich and Shreyasi Datta, Good functions, measures, and the Kleinbock-Tomanov conjecture, https://arxiv.org/abs/2209.10456.

55) With Prasuna Bandi and Debanjan Nandi, Exact approximation order and well-distributed sets, to appear in Advances in Mathematics.

54) With V. Vinay Kumaraswamy, Some new results in quantitative Diophantine approximation, to appear in International Mathematics Research Notices.

53) With Mahbub Alam and Jiyoung Han, Higher moment formulae and limiting distributions of lattice points, to appear in Journal of the Institute of Mathematics of Jussieu. 

52) With Jiyoung Han, Values of inhomogeneous forms at S-integral points, Mathematika, 68 (2022), no. 2, 565–593.

51) With Alexander Gorodnik and Amos Nevo, Counting intrinsic Diophantine approximations in simple algebraic groups, Israel Journal of Mathematics, 251, pages 443–466 (2022).

50) With Mahbub Alam and Shucheng Yu, Quantitative Diophantine approximation with congruence conditions, Journal de Théorie des Nombres de Bordeaux, Tome 33, no 1 (2021), p. 261-271.

49) With Prasuna Bandi, Small solutions of quadratic forms with congruence conditions, https://arxiv.org/abs/2008.08568, submitted. 

48) With Prasuna Bandi and Jiyoung Han, A generic effective Oppenheim theorem for systems of forms, Journal of Number Theory, 218 (2021), 311-333.

47) With Mahbub Alam, Quantitative rational approximation on spheres,  Selecta Math. (N.S.) 28 (2022), no. 5, Paper No. 86, 22 pp.

46) With Dubi Kelmer and Shucheng Yu, Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts, to appear in International Mathematics Research Notices.

45) With Dubi Kelmer and Shucheng Yu, Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts, International Mathematics Research Notices, Volume 2022, Issue 6, March 2022, Pages 4682-4719.

44) With Debanjan Nandi, Diophantine Approximation, large intersections and geodesics in negative curvature, https://arxiv.org/abs/1911.01406, submitted. 

43) With Shreyasi Datta, Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents, Bull. Soc. Math. France148 (4), 2020, p. 733-747.

42) With Prasuna Bandi, On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form, Mathematische Zeitschrift volume 299, pages781-796 (2021).

41) With Maxim Kirsebom and Parthanil Roy, Continued fractions, the Chen-Stein method and extreme value theory, Ergodic Theory and Dynamical Systems, Volume 41, Issue 2, February 2021 , pp. 461-470.

40) With Shreyasi Datta, Diophantine inheritance for p-adic measures, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)Vol. XXIII (2022), 49-80.

39) With Arijit Ganguly, The inhomogeneous Sprindzhuk conjecture over a local field of positive characteristic, Dynamics: topology and numbers, 191–203, Contemp. Math., 744, Amer. Math. Soc. 2020.

38) With Mahbub Alam, Equidistribution on homogeneous spaces and the distribution of approximates in Diophantine approximation, Trans. Amer. Math. Soc. 373 (2020), 3357-3374. 

37) Topics in homogeneous dynamics and number theory, Elements of dynamical systems, 165–186, Texts Read. Math., 79, Hindustan Book Agency, Delhi, [2020]. 

36) With S. Chow, L. Guan, A. Marnat and D. Simmons, Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. XXI (2020), 643-671.

35) With Shreyasi Datta, S-arithmetic  Inhomogeneous Diophantine approximation on manifolds, to appear in Advances in Mathematics.

34) With Alexander Gorodnik and Amos Nevo, Optimal density for values of generic polynomial maps, American Journal of Mathematics Volume 142, Number 6, December 2020, 1945-1979.

33) With Jinpeng An, Lifan Guan and Tue Ly, Bounded orbits of Diagonalizable Flows on finite volume quotients of products of SL(2, R), Advances in Mathematics, 354 (2019).

32) With V. Beresnevich, A. Ganguly and S. Velani, Inhomogeneous dual Diophantine approximation on affine subspaces, International Mathematics Research Notices Volume 2020, Issue 12, June 2020, Pages 3582--3613.

31) With Arijit Ganguly, Remarks on Diophantine approximation in function fields, Math. Scand. 124 (2019), 5-14. 

30) With V. Beresnevich, D. Simmons and S. Velani, Diophantine approximation in Kleinian groups: singular, extremal and bad limit points, J. London Math. Soc. (2) 98, (2018), 306–328.

29) With Antoine Marnat, On Diophantine transference principles, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 166, Issue 3 May 2019 , pp. 415-431.

28) With Stephan Baier, Inhomogeneous Diophantine approximation with prime constraints,  Proc. Indian Acad. Sci. Math. Sci. 128 (2018), no. 4, Art. 44.

27) With Arijit Ganguly, Quantitative Diophantine approximation on affine subspaces, Mathematische Zeitschrift, 292(3), (2019), 923-935.

26) With Dubi Kelmer, A quantitative Oppenheim Theorem for generic ternary quadratic forms,  Journal of Modern Dynamics Volume 12, 2018, 1–8.

25) Diophantine approximation on subspaces of R^n and dynamics on homogeneous spaces, Handbook of Group Actions (Vol. IV) ALM 41, Ch. 9, pp. 509–527. Editors Lizhen Ji, Athanase Papadopoulos, Shing- Tung Yau.

24) With Jayadev Athreya, The Erdös-Szüsz- Turan distribution for equivariant processes, L’Enseignement Mathématique (2) 64 (2018), 1–21.

23) With Dubi Kelmer, Shrinking Targets for semisimple groups, Bulletin of the London Mathematical Society, Vol: 49 (2017), Pages: 235–245.

22) With Arijit Ganguly, Dirichlet’s theorem in function fields, Canadian Journal of Mathematics, 69 (2017), 532-547.

21) With Stephan Baier, Restricted simultaneous Diophantine approximation, Mathematika, volume 63, issue 01, 34-52.

20) With Jayadev Athreya and Kingshook Biswas, Cusp excursions on hyperbolic manifolds, to appear in Teichmüller theory and its impact, Editors Lizhen Ji, Athanase Papadopoulos, Weixu Su.

19) With Alexander Gorodnik and Amos Nevo, Best possible rates of distribution of dense lattice orbits in homogeneous spaces, J. reine angew. Math, Volume 2018, Issue 745, Pages 155-188.

18) With Jayadev Athreya and Jimmy Tseng, Spherical averages of Siegel transforms for higher rank diagonal actions and applications, https://arxiv.org/abs/1407.3573.

17) With Alexander Gorodnik and Amos Nevo, Diophantine approximation exponents on homogeneous varieties, Contemp. Math. 631 (2015) 181-200.

16) With Manfred Einsiedler and Beverly Lytle, Badly approximable vectors, C^1 curves and number fields, Ergodic Theory and Dynamical Systems, volume 36, issue 06, pp. 1851-1864.

15) With Stephan Baier, Diophantine approximation on lines with prime constraints, The Quarterly Journal of Mathematics, 66 (1) (2015), 1-12.

14) With Jayadev Athreya and Jimmy Tseng, Spherical averages of Siegel transforms and spiraling of lattice approximations, J. London Math. Soc. (2) 91 (2015), 383-404

13) With Robert Royals, An extension of Khintchine's theorem, Acta Arithmetica, 167 (2015), 1-17.

12) With Jayadev Athreya and Amritanshu Prasad, Buildings, Extensions and Volume Growth Entropy, New York J. Math. 19 (2013), 1-11.

11) With Alexander Gorodnik and Amos Nevo, Metric Diophantine approximation on homogeneous varieties, Compositio Mathematica, Volume 150, no. 08 (2014), 1435-1456.

10) With Alan Haynes, Projective Metric Number Theory, J. reine angew. Math. 712 (2016), 39–50.

9) With Jayadev Athreya and Amritanshu Prasad, Ultrametric logarithm laws, II, Monatsh. Math. 167 (2012), no. 3, 333-356.

8) With Alexander Gorodnik and Amos Nevo, Diophantine approximation and automorphic spectrum, IMRN (2013) Vol 21, 5002-5058.

7) Diophantine exponents and the Khintchine Groshev theorem, Monatsh. Math. 163 (2011), no. 3, 281-299.

6) A Khintchine Groshev theorem for affine hyperplanes, Int. J. Number Theory, 7 (2011), no. 4, 1045- 1064.

5) Diophantine approximation on affine hyperplanes, Acta Arithmetica, 144 (2010), 167-182.

4) With Manfred Einsiedler, Rigidity of measures invariant under semisimple groups in positive characteristic, Proc. London Math. Soc. (3) 100 (2010). no. 1, 249-268.

3) With Jayadev Athreya and Amritanshu Prasad, Ultrametric logarithm laws, I, Discrete Cont. Dyn. Sys. Series S, 2 (2009), no. 2, 337-348.

2) Metric Diophantine approximation over a local field of positive characteristic, Journal of Number Theory, 124 (2007), no. 2, 454-469.

1) A Khintchine-type theorem for hyperplanes, J. London Math. Soc. (2) 72 (2005). no. 2, 293-304.

Books and miscellanea 

4) Weyl's theorem on equidistribution of sequences. Expository article for college students.

3) Geometric and Ergodic Aspects of Group Actions. Edited by S. G. Dani and A. Ghosh. Infosys Science Foundation Series in Mathematical Sciences, Springer Verlag, 2019.

2) Recent Trends in Ergodic Theory and Dynamical Systems, Contemporary Mathematics Volume: 631; 2015. Edited by S. Bhattacharya, T. Das, A. Ghosh and R. Shah.

1) Density, Duality, Spectra, Oberwolfach reports, 2010.

Support

My work is currently supported by a DST Swarnajayanti fellowship, a grant from the Infosys foundation, a MATRICS grant from SERB and a CEFIPRA grant, in addition to support from the Tata Institute. Past support include grants from the UGC, (US)NSF, (UK)EPSRC and the (UK)Royal Society. All support is gratefully acknowledged.