Research Papers.
Preprints and Works in-progress:
(with Neil Dummigan) "Modular Elliptic Curves and Hyperbolic Uniformization" (under-review, arXiv: 2607.03830)
(with Harshvardan Reddy) ``Shimura Curves and Heun functions" (preprint, arxiv: 2608.14495).
(with Helena Verrill ) ``Farey Symbols for Picard Group $PSL(2, Z[i])$"} (in preparation).
Hecke Triangle Groups and Bipartite q-boid Graph (preprint, arXiv: 2112.06770).
(with Yifan Yang) ``Shimura Curves and Algebraic Values of Hypergeometric functions", (in preparation).
Published/Accepted:
(with Harshvardhan Reddy) “Revisiting Kulkarni's Topological proof of Millington's Theorem”, Groups and Mathematical Philosophy, Contemporary Mathematics, vol. 811, Amer. Math. Soc., Providence, RI, 2025, pp. 241-257.
A Shimizu Type Theorem for Subgroups in Sp(n, 1), The Math Student, Vol. 93, (2024), 101-115.
(with Sagar Kalane) On Free Group Generated by Two Heisenberg Translations. Proc. Indian Acad. Sci. Math. Sci. 132 (2022), no. 1, Paper No. 38, 10 pp.
(with Krishnendu Gongopadhyay and Abhishek Mukherjee) Discreteness of hyperbolic isometries by test maps. Osaka J. Math. 58 (3), 697-710, (July 2021).
(with Vijay Kumar Sohani) Dispersion Estimates for the Discrete Hermite Operator. Indian J. Pure Appl. Math. 52 (2021), no. 3, 773–786.
(with Krishnendu Gongopadhyay and Mukund Madhav Mishra) On Discreteness of Subgroups of Quaternionic Hyperbolic Isometries. Bull. Aust. Math. Soc. 101 (2020), no. 2, 283--293.
(with Krishnendu Gongopadhyay and Mukund Madhav Mishra) ON GENERALIZED JORGENSEN INEQUALITY IN SL(2, C). Siberian Electronic Mathematical Reports, Vol 16 (2019), 542--546.
Edited Books:
``Modularity and Generalized Fermat Equations", Edited with Mike Bennett, Henri Darmon, Sujatha Ramdorai, Samir Siksek, and Dinesh Thakur, CRM Proceedings, Contemp. Math., 849, 2026; 317 pp. AMS, Providence, RI, 2026.
``Arithmetic and Geometry of Calabi-Yau three-folds",Edited with Charles Doran, Ling Long, Noriko Yui, Dinesh Thakur. (accepted for publication by International Press)
Miscellaneous:
Interview with Gerald Folland, Professor Emeritus, University of Washington in Bhavana Magazine, volume 2, issue 3, July 2018.
Selected Invited Talks:
1. Heun Functions and Shimura Curves of Discriminant 14 and 15., 18th May 2026, GADEP Smeinars, IMPA Brazil (Online talk).
2. Hypergeometric Abelian Varieties and Generalized Fermat equations, 2nd December 2025,
Scuola Normale Superiore, University of Pisa.
3. Hypergeometric Functions, Triangle Groups, and Fermat type Equations, 17 April 2025, NTU Taiwan.
4.Hypergeometric Functions, Triangle Groups and Fermat type Equations}, 8th Nov 2024, HRI Prayagraj.
5.Constructing Bipartite Graphs for certain Triangle Groups, 18th Oct. 2023 at IISER Pune.
6. Triangle Groups and Generalised Fermat Equation: x^p + y^q = z^r, 1st Sep, 2023 at ISI Delhi.
7. Hecke Triangle Groups and Dessin d’enfant, 29th August, 2023 at IIT Delhi.
8. Role of Geometry in the Study of Fermat-like Equations, 24th August, 2023 at IISER Tirupati.
9. A Topological Way to Classify Modular Subgroups, 22nd August, 2023 at IIT Tirupati.
10. Hecke Triangle Groups and Dessin d’enfant, 10th August, 2023 at IIT Gandhinagar.
11. Modular Subgroup and Drawings, 21st June, 2023 at IIT Indore
12. Branched Riemann Surfaces: Theory and Application, 18th November 2022, a seminar talk at IISER Pune.
13. Modular Group and Drawings, May-25th 2022, a virtual talk in the conference at BP, Pune
in honor of the 80th birthday of Professor Ravindra S. Kulkarni. YT link of talk
Workshop and Conferences attended.
ICTP Winter School in Number Theory and Physics, Trieste, Italy, Nov 17 - 28, 2025.
Recent Advances in Anabelian Geometry and Related Topics at ICMS Edinburgh, April 27 -May 2, 2025,.
Lecture series by Minhyong Kim on Arithmetic Geometry and QFT at ICTS Bengaluru, Sep 2-9, 2024.
Zariski Dense Subgroups, Number Theory and Geometric Applications, ICTS Bengaluru , Jan 1-12, 2024 .
Conference on Harish-Chandra's Birth Centenary at HRI, Prayagraj, 9-14th Oct 2023.
Workshop on Representation Theory of Real Lie Groups at HRI, Prayagraj, Oct 2-7th, 2023 .
Topics in Birational Geometry, ICTS Bangalore, 27-31 January, 2020.
Advanced Instructional School in Riemannian Geometry, IISc Bangalore, July-2019.
NCM Workshop on Characteristic Classes and Cobordism, IIT Bombay, March-2019.
Advanced Instructional School on Harmonic Analysis, NISER Bhubaneswar, December-2018.
Discussion Meeting in Harmonic Analysis (DMHA), IISc. Bangalore, December-2017.
Surface Group Representations and Geometric Structures, ICTS Bangalore, INDIA, November-2017.
Geometry, Groups and Dynamics, ICTS Bangalore, INDIA, November-2017.
Advanced Instructional School on Harmonic Analysis, KSOM, Kerala, December-2016.
Advanced Instructional School on Differential Geometry, IIT Bombay, May-2016.
Discussion Meeting in Harmonic Analysis (DMHA), Delhi University, December-2015.
International Conference: Topology and Groups, Goa University, INDIA, October-2015.
ATM Workshop: Lattices: Geometry and Dynamics (GAAHS Part 2), IISER Mohali, INDIA, December-2014.
Geometry and Analysis of Hyperbolic Spaces (GAAHS Part 1), Delhi University, INDIA, December-2014.
Advanced School and Discussion Meeting on Knot Theoty and its Applications, IISER Mohali, INDIA, December-2013. (ICTS Program)
Teichmuller Theory and Interfaces with Ergodic Theory and Group Actions, JNU Delhi, INDIA, October-2013.
ATM Workshop on Classification of Manifolds, NEHU, Shillong, June-2013.
Annual Foundation School, Part 3, HRI Allahabad, INDIA, July-2012.
ATM Workshop on Differential Geometry, BHU, Varanasi, May-2011.
ATM Workshop on Hyperbolic Geometry and Geometric Complex Analysis, Delhi University, March-2011.
Summer Programme in Mathematics (SPIM), HRI Allahabad, INDIA, June-2010.
Summer School on Gravitation and Cosmology, HRI Allahabad, May-2010.