# Maleeha Khawaja

I'm a final year PhD student, at the University of Sheffield, working in number theory. My supervisor is Dr. Frazer Jarvis. I am due to graduate in Summer 2024.

I previously completed my MSc at the University of Nottingham under the supervision of Dr. Christian Wuthrich. Prior to that, I completed my maths undergraduate degree at the University of Warwick.

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

Email: msurname2 at sheffield dot ac dot uk

Github: github.com/MaleehaKhawaja

# Papers

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

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

On perfect powers that are sums of cubes of a nine term arithmetic progression. arXiv. With Nirvana Coppola, Mar Curcó Iranzo, Vandita Patel, and Özge Ülkem. Accepted in Indagationes Mathematicae.

Primitive algebraic points on curves. arXiv. With Samir Siksek. Submitted.

Torsion primes for elliptic curves over degree 8 number fields. arXiv. Accepted in Research in Number Theory.

Power values of power sums: a survey. arXiv. With Nirvana Coppola, Mar Curcó Iranzo, Vandita Patel, and Özge Ülkem. Accepted in "Women in Numbers Europe 4 - Research Directions in Number Theory", Association for Women in Mathematics Series, Springer.

Fermat's Last Theorem over Q(sqrt2, sqrt3). arXiv. With Frazer Jarvis. Submitted.

# Invited Talks

Primitive algebraic points on curves

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, 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(sqrt2, sqrt3): 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)