# 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 Autumn 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. Submitted.

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 -- Manchester Number Theory Seminar, University of Manchester -- October 2023

Primitive algebraic points on curves -- Northern Number Theory Seminar, University of Sheffield -- September 2023

Primitive algebraic points on curves -- 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 – Nottingham Number Theory Seminar (University of Nottingham) – March 2023

The Fermat equation over real biquadratic fields – Warwick Junior Number Theory Seminar (University of Warwick) – January 2023

The Fermat equation over real biquadratic fields – Linfoot Number Theory Seminar (University of Bristol) – October 2022

A uniform approach to Diophantine equations – Women In Numbers Europe 4 (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 (lying in a quadratic extension of Q(sqrt2)) – Women in Number Theory and Geometry – Apr' 2023

Fermat's Last Theorem over Q(sqrt2, sqrt3): some small prime exponents – ENTR workshop (TU Darmstadt) – Oct’ 2022

The Fermat equation over real biquadratic fields – Sheffield Number Theory Seminar (University of Sheffield) – Oct’ 2022

Presheaves & Sheaves - Sheffield Algebraic Geometry Reading Group – Oct’ 2021

The Fermat equation over real biquadratic fields – Young Researchers in Algebraic Number Theory (Online) – Aug’ 2021

l-adic Galois representations – Sheffield Number Theory Reading Group – Mar’ 2021

Elliptic Curves and the Congruent Number Problem – Sheffield PGR Student Seminar – Oct’ 2020