# Maleeha Khawaja

I'm currently a Research Associate, at the University of Bristol, working with Dr. Céline Maistret. From October 2020 - April 2024, I was a PhD student at the University of Sheffield under the supervision of Dr. Frazer Jarvis. I passed my viva in July 2024.

My interests lie in the global and local arithmetic of curves, rational points on curves, computational number theory and the explicit resolution of Diophantine equations.

Email: firstname.surname@bristol.ac.uk / msurname2@sheffield.ac.uk

Github: github.com/MaleehaKhawaja

# Papers

The modular approach to Diophantine equations over totally real fields. With S. Siksek. Submitted. arXiv.

A single source theorem for primitive points on curves. With S. Siksek. Submitted. arXiv.

On perfect powers that are sums of cubes of a nine term arithmetic progression. With N. Coppola, M. C. Iranzo, V. Patel, and Ö. Ülkem. Indagationes Mathematicae 35, 3 (2024). link. arXiv.

Primitive algebraic points on curves. With S. Siksek. Research in Number Theory 10, 57 (2024). link. arXiv.

Torsion primes for elliptic curves over degree 8 number fields. Research in Number Theory 10, 48 (2024). link. arXiv.

Power values of power sums: a survey. With N. Coppola, M. C. Iranzo, V. Patel, and Ö. Ülkem. Women in Numbers Europe IV. Association for Women in Mathematics Series, vol. 32. link. arXiv.

Fermat's Last Theorem over Q(√2,√3). With F. Jarvis. To appear in Algebra & Number Theory. arXiv.

# Invited Talks

Primitive algebraic points on curves

University of Zagreb Number Theory Seminar (May 2024)

University of Manchester Number Theory Seminar (October 2023)

Northern Number Theory Seminar, University of Sheffield (September 2023)

Arithmetic Geometry Workshop, Trinity College Dublin (June 2023)

International Women in Mathematics Day celebration, University of Sheffield (May 2023)

The Fermat equation over real biquadratic fields

University of Nottingham Number Theory Seminar (March 2023)

University of Warwick Junior Number Theory Seminar (January 2023)

University of Bristol Linfoot Number Theory Seminar (October 2022)

A uniform approach to Diophantine equations, Women In Numbers Europe 4, Universiteit Utrecht (with Nirvana Coppola, Mar Curcó-Iranzo and Özge Ülkem, September 2022)

# Contributed Talks

Primitive algebraic points on curves. The Mordell conjecture: 100 years later, Lightning talk, MIT (July 2024)

Primitive algebraic points on curves. Rational Points 2023, Franken-Akademie Schloss Schney (July 2023)

Quartic points on the Fermat quartic. Women in Number Theory and Geometry (April 2023)

Fermat's Last Theorem over Q(√2,√3): some small prime exponents. ENTR workshop, TU Darmstadt (October 2022)

The Fermat equation over real biquadratic fields. University of Sheffield Number Theory Seminar (October 2022)

Presheaves & Sheaves. University of Sheffield Algebraic Geometry Reading Group (October 2021)

The Fermat equation over real biquadratic fields. Young Researchers in Algebraic Number Theory (Online) (August 2021)

l-adic Galois representations. University of Sheffield Number Theory Reading Group (March 2021)

Elliptic Curves and the Congruent Number Problem. University of Sheffield PGR Student Seminar (October 2020)