# Anish Ghosh अनीश घोष অনীশ ঘোষ

I am an Associate Professor in the School of Mathematics, TIFR.

Office: Room A330. Email: lastname@math.tifr.res.in. Phone: 91-22-22782282

I am interested in the ergodic theory of group actions on homogeneous spaces and interactions with number theory.

I am on the faculty search committee. If you'd like to apply for a position, do get in touch.

This semester, the ergodic theory seminar meets at 2:00 pm every Thursday in room AG77 of the Institute.

Current students: Shreyasi Datta, Prasuna Bandi, Mahbub Alam, Rajdip Palit (Rajdip is a student at JNU, jointly supervised by Riddhi Shah and me). Former students.

Recent and Upcoming Events:

Distinguished lectures in Dynamics, 2017

Geometric And Ergodic Aspects of Group Actions 2015

Interactions between Dynamics of Group Actions and Number Theory 2014

Recent Teaching:

- Spring 2018, Minicourse "Ergodic theory", University of Pune.
- Winter 2017, Minicourse "Arithmetic Dynamics", IIT Delhi.
- Fall 2017, Dynamical Systems on homogeneous spaces of Lie groups.
- Summer 2017, Minicourse "Dynamics of group actions on homogeneous spaces" Houston, TX.
- Spring 2017, Minicourse "Dynamics on homogeneous spaces and Diophantine approximation" CIRM Luminy.
- Spring 2016 Expander Graphs, taught jointly with Prahladh Harsha.
- Fall 2015 Real Analysis.

Preprints and Publications:

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

- With S. Chow, L. Guan, A. Marnat and D. Simmons, Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents, submitted.
- With Shreyasi Datta, S-arithmetic Inhomogeneous Diophantine approximation on manifolds, submitted.
- With Alexander Gorodnik and Amos Nevo, Optimal density for values of generic polynomial maps, submitted.
- With Jinpeng An, Lifan Guan and Tue Ly, Bounded orbits of Diagonalizable Flows on finite volume quotients of products of SL(2, R), submitted.
- With V. Beresnevich, A. Ganguly and S. Velani, Inhomogeneous dual Diophantine approximation on affine subspaces, to appear in International Mathematics Research Notices.
- With Arijit Ganguly, Remarks on Diophantine approximation in function fields, to appear in Mathematica Scandinavica.
- 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.
- With Antoine Marnat, On Diophantine transference principles, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
- With Stephan Baier, Inhomogeneous Diophantine approximation with prime constraints, Proc. Indian Acad. Sci. Math. Sci. 128 (2018), no. 4, Art. 44.
- With Arijit Ganguly, Quantitative Diophantine approximation on affine subspaces, to appear in Mathematische Zeitschrift.
- With Dubi Kelmer, A quantitative Oppenheim Theorem for generic ternary quadratic forms, Journal of Modern Dynamics, Volume 12, 2018, 1–8.
- 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.
- With Jayadev Athreya, The Erdös-Szüsz- Turan distribution for equivariant processes, to appear in L’Enseignement Mathématique.
- With Dubi Kelmer, Shrinking Targets for semisimple groups, Bulletin of the London Mathematical Society, Vol: 49 (2017), Pages: 235–245.
- With Arijit Ganguly, Dirichlet’s theorem in function fields, Canadian Journal of Mathematics, 69 (2017), 532-547.
- With Stephan Baier, Restricted simultaneous Diophantine approximation, Mathematika, volume 63, issue 01, 34-52.
- 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.
- With Alexander Gorodnik and Amos Nevo, Best possible rates of distribution of dense lattice orbits in homogeneous spaces, J. reine angew. Math, DOI: 10.1515/crelle-2016-0001.
- With Jayadev Athreya and Jimmy Tseng, Multiparameter spherical averages of Siegel transforms and applications, submitted.
- With Alexander Gorodnik and Amos Nevo, Diophantine approximation exponents on homogeneous varieties, Contemp. Math. 631 (2015) 181-200.
- 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.
- With Stephan Baier, Diophantine approximation on lines with prime constraints, The Quarterly Journal of Mathematics, 66 (1) (2015), 1-12.
- 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
- With Robert Royals, An extension of Khintchine's theorem, Acta Arithmetica, 167 (2015), 1-17.
- With Jayadev Athreya and Amritanshu Prasad, Buildings, Extensions and Volume Growth Entropy, New York J. Math. 19 (2013), 1-11.
- With Alexander Gorodnik and Amos Nevo, Metric Diophantine approximation on homogeneous varieties, Compositio Mathematica, Volume 150, no. 08 (2014), 1435-1456.
- With Alan Haynes, Projective Metric Number Theory, J. reine angew. Math. 712 (2016), 39–50.
- With Jayadev Athreya and Amritanshu Prasad, Ultrametric logarithm laws, II, Monatsh. Math. 167 (2012), no. 3, 333-356.
- Density, Duality, Spectra, Oberwolfach reports, 2010.
- With Alexander Gorodnik and Amos Nevo, Diophantine approximation and automorphic spectrum, IMRN (2013) Vol 21, 5002-5058.
- Diophantine exponents and the Khintchine Groshev theorem, Monatsh. Math. 163 (2011), no. 3, 281-299.
- A Khintchine Groshev theorem for affine hyperplanes, Int. J. Number Theory, 7 (2011), no. 4, 1045- 1064.
- Diophantine approximation on affine hyperplanes, Acta Arithmetica, 144 (2010), 167-182.
- With Manfred Einsiedler, Rigidity of measures invariant under semisimple groups in positive characteristic, Proc. London Math. Soc. (3) 100 (2010). no. 1, 249-268.
- With Jayadev Athreya and Amritanshu Prasad, Ultrametric logarithm laws, I, Discrete Cont. Dyn. Sys. Series S, 2 (2009), no. 2, 337-348.
- Metric Diophantine approximation over a local field of positive characteristic, Journal of Number Theory, 124 (2007), no. 2, 454-469.
- A Khintchine-type theorem for hyperplanes, J. London Math. Soc. (2) 72 (2005). no. 2, 293-304.