Research

My research interests involve rational points on abelian varieties, modular curves, and modular forms. In particular, I study rational generalizations of Ogg's Conjecture; that is torsion points on (generalized) Jacobians of modular curves. In the past, I wrote my master's thesis on the relation between Weierstrass points on the modular curves X0(p) and supersingular elliptic curves over finite fields. I'm also interested in diophantine equations and elliptic K3 surfaces. 

Publications and Preprints

• Rational torsion of generalised modular Jacobians with odd level. (2022) https://arxiv.org/abs/2112.03741 

This work superseded my previous work: Rational torsion of generalised modular Jacobians of level divisible by two primes. (2021) 

• Power values of power sums: a survey. (2023)  Joint work with Nirvana Coppola, Maleeha Khawaja, Vandita Patel and Özge Ülkem. https://arxiv.org/abs/2306.05168

• On perfect powers that are sums of cubes of a nine term arithmetic progression. (2023) Joint work with Nirvana Coppola, Maleeha Khawaja, Vandita Patel and Özge Ülkem. 

Upcoming works

Thesis

•  Weierstrass points on modular curves and supersingular elliptic curves. (2020) Master's Thesis written under the supervision of Gunther Cornelissen.