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.
Research in the Mathematical Sciences (2025), ArXiv, journal.
This work superseded my previous work: Rational torsion of generalised modular Jacobians of level divisible by two primes.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 with Nirvana Coppola, Maleeha Khawaja, Vandita Patel and Özge Ülkem.
Women in Numbers Europe IV. Association for Women in Mathematics Series, Springer (2023), ArXiv, book.
On perfect powers that are sums of cubes of a nine term arithmetic progression with Nirvana Coppola, Maleeha Khawaja, Vandita Patel and Özge Ülkem.
Indagationes Mathematicae (2024), ArXiv, journal.
Conductor exponents for families of hyperelliptic curves (2024) with Martin Azon, Maleeha Khawaja, Céline Maistret and Diana Mocanu. ArXiv
Submitted
Rational torsion of generalised Drinfeld modular Jacobians of prime power level (2024) ArXiv
Submitted
Experimental investigations on Lehmer's Conjecture for elliptic curves with Sven Cats, John Clark, Charlotte Dombrowsky, Krystal Maughan and Eli Orvis.
Accepted to LMFDB, Computation, and Number Theory.
Thesis
Exploring the arithmetic of generalised modular Jacobians and of power sums (2025), PhD thesis written under the supervision of Valentijn Karemaker.
Weierstrass points on modular curves and supersingular elliptic curves (2020), Master's Thesis written under the supervision of Gunther Cornelissen.