Research Papers.

Preprints:

1. (with Fang-Ting Tu) "Computing Belyi maps for certain Shimura Curves" (in preparation).

2. (with Ravi S. Kulkarni) “On Cycloidal and Semi-Cycloidal Subgroups of Modular Group”, (in preparation).

3. “Hypergeometric Abelian Varieties and Diophantine Applications” with Fang-Ting Tu (in preparation).

4. Hecke Triangle Groups and Bipartite q-boid Graph (preprint).
   
   Published/Accepted:

1. (with Harshvardhan Reddy) “Revisiting Kulkarni's Topological proof of Millington's Theorem”, accepted for publication in ``Geometry and Symmetry'', Contemporary Math., Amer. Math. Soc., Providence, RI, 2024.

2. A Shimizu Type Theorem for Subgroups in Sp(n, 1), accepted for publication in Math. Student 2024.

3. (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.

4. (with Krishnendu Gongopadhyay and Abhishek Mukherjee) Discreteness of hyperbolic isometries by test maps. Osaka J. Math. 58 (3), 697-710, (July 2021).

5. (with Vijay Kumar Sohani) Dispersion Estimates for the Discrete Hermite Operator. Indian J. Pure Appl. Math. 52 (2021), no. 3, 773–786.

6. (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.

7. (with Krishnendu Gongopadhyay and Mukund Madhav Mishra) ON GENERALIZED JORGENSEN INEQUALITY IN SL(2, C). Siberian Electronic Mathematical Reports, Vol 16 (2019), 542--546.

Under-preparation Books:

1. ``Modularity and Generalized Fermat Equations", proceedings of the second trimester of the year long program on Triangle Groups, Belyi Uniformization and Modularity (preprint).

2. ``Arithmetic and Geometry of Calabi-Yau three-folds", proceedings of the third trimester of the year long program on Triangle Groups, Belyi Uniformization and Modularity.

Miscellaneous:

Interview with Gerald Folland, Professor Emeritus, University of Washington in Bhavana Magazine, volume 2, issue 3, July 2018.

Talks:

1. Constructing Bipartite Graphs for certain Triangle Groups, 18th Oct. 2023 at IISER Pune.
2. Triangle Groups and Generalised Fermat Equation: x^p + y^q = z^r, 1st Sep, 2023 at ISI Delhi.
3. Hecke Triangle Groups and Dessin d’enfant, 29th August, 2023 at IIT Delhi.
4. Constructing Bipartite Graphs for Hecke Triangle Groups, 25th Aug, 2023 at IISER Tirupati.
5. Role of Geometry in the Study of Fermat-like Equations, 24th August, 2023 at IISER Tirupati.
6. A Topological Way to Classify Modular Subgroups, 22nd August, 2023 at IIT Tirupati.
7. Triangle Groups and Darmon’s Program for the Generalized Fermat Equation: x^p + y^q = z^r, 17th August, 2023 at IIT Goa.
8. Hecke Triangle Groups and Dessin d’enfant, 10th August, 2023 at IIT Gandhinagar.
9. Modular Subgroup and Drawings, 21st June, 2023 at IIT Indore 

10. Branched Riemann Surfaces: Theory and Application, 18th November 2022, a seminar talk at IISER Pune.

11. 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

12. Dispersion Estimates for the Discrete Hermite Operator, August 3rd 2021, Symposium in Number Theory at BP Pune,
in honor of the 60th birthday of Professor Dinesh Thakur.

13. Teaching Mathematics Using Technology, January 15th 2021, a virtual talk
for nationwide CBSE school teachers from 6th to 12th standard.

14. Actions of Discrete Groups on Hyperbolic Spaces, September 26, 2018, Graduate students seminar at IISER Mohali, Mohali. 

15. Role of Parallel Postulate in Geometry, 27 Jan, 2015 at Mathematics Seminar, Indraprastha College for Women, Delhi University.

16. Topology of Classical Groups, April 25, 2014 at Research Scholar Seminar, Department of Mathematics, Delhi University, Delhi.

17. Hopf Fibration,  April 16, 2014 at Research Scholar Seminar, Department of Mathematics, Delhi University, Delhi.

Workshop and Conferences attended.

• 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.