Research

I am interested in Computational Algebraic Number Theory and Arithmetic Geometry, Elliptic Curves, Rational points on Curves, Galois Representations, Diophantine Equations, Modular Forms and Cryptography.

In Preparation:

1. Chabauty-Coleman method, modular approach and applications to Lebesgue-Nagell equations, in preparation.

2. On the solution of a family of generalized Lebesgue-Nagell equations using Frey hyperelliptic curves, in preparation.

3. Picard curves with good reduction at two small primes, in preparation (joint with Irene Bouw, Jeroen Sijsling, Stefan Wewers).

Papers and Preprint:

1. Darmon's Program: A survey, accepted to BP Proceedings (joint with Imin Chen). Preprint here.

2. A modular approach to Fermat equations of signature (p,p,5) using Frey hyperelliptic curves, (joint with Imin Chen), submitted, arXiv.

3. Appendix to: Weak Approximation to 0-cycles on a product of elliptic curves, by Evangelia Gazaki, Math. Annalen, 2022, arXiv.

4. Perfect powers in sum of three fifth powers, Journal of Number Theory, 2021, (joint with Pranabesh Das, Pallab Kanti Dey, Nikolaos Tzanakis), arXiv.

5. The equation (x-d)5 + x5 + (x+d)5 = yn,  Acta Arithmetica,  2021, (joint with Michael Bennett), arXiv.

6. Conductor and discriminant of Picard curves,  Journal of London Math. Soc., 2020, (joint with Irene Bouw, Jeroen Sijsling, Stefan Wewers), arXiv.

7. A robust implementation for solving S-unit equations and several applications, Arithmetic Geometry, Number Theory, and Computation, Simons Symposia Series (joint with Alejandra Alvarado, Beth Malmskog, Christopher Rasmussen, Christelle Vincent, Mckenzie West), arXiv.

8. On the generalized Fermat equation a2+3b6=cn, Bulletin of the Hellenic Math. Soc., 2020, arXiv, code.

9. An application of the modular method and the symplectic argument to a Lebesgue-Nagell equation , Mathematika, 2019, arXiv, code.

10. On the solutions of the Diophantine equation (x-d)2 + x2 + (x+d)2 = yn for d a prime power, Funct. Approx. Comment. Math., 2021, arXiv, code.

11. Perfect powers that are sums of squares in a three term arithmetic progression, Int. J. Number Theory, 2018, (joint with Vandita Patel), arXiv, code.

12. Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction, Experimental Mathematics, 2019, arXiv.

You can also find my papers in my google scholar and orcid.