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Josha Box

Swiss Alps

About me

As of October 2017, I am a PhD student in Number Theory at Warwick under the supervision of Prof. Samir Siksek.

My origins lie in Amsterdam, where I completed my MSc in Mathematics in 2017 at the University of Amsterdam. In between the two MSc years, I took a year off to do Part III in Cambridge.

Research interests

I spend most of my time thinking about points on (modular) varieties. Most recently, low degree points on modular curves using Chabauty's method, and integral points on Hilbert and Siegel modular varieties.

Papers

2021: Elliptic curves over totally real quartic fields not containting root 5 are modular (in preparation).

2021: Cubic and quartic points on modular curves using generalised symmetric Chabauty (in preparation), joint with Stevan Gajović and Pip Goodman .

2021: Computing models for quotients of modular curves (arXiv).

2020: Bounding integral points on the Siegel modular variety A_2(2) (arXiv), joint with Samuel le Fourn.

2019: Quadratic points on modular curves with infinite Mordell--Weil group (arXiv), published in Mathematics of Computation.

Other work

2018: PhD first year report (pdf)

2017: Height Bounds for Mordell equations using Modularity (master's thesis under the supervision of Dr. Sander Dahmen, pdf  )

2016: Bounded Intervals Containing Primes (Part III essay under the supervision of Dr. Adam Harper, pdf  ).

2014: An Introduction to Skolem's p-adic Method for solving Thue Equations (Bachelor's thesis under the supervision of Dr. Sander Dahmen, pdf  ).

Slides

Slides for the talk I gave in Bristol on May 6, 2020: here.

Lecture notes

For a preparatory course for the IMC in Amsterdam, Iris Smit and I have written lecture notes (in Dutch).

Contact

E-mail: J.Box *at* warwick.ac.uk

My office in the maths department in Warwick is B0.15.