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Josha Box

Swiss Alps

About me

Between 2017 and 2021, I was a PhD student in Number Theory at Warwick supervised by Prof. Samir SiksekLink opens in a new window. On this page you can find links to my work.

Papers

2021: Elliptic curves over totally real quartic fields not containting root 5 are modular (arXivLink opens in a new window), published in Transactions of the American Mathematical Society.

2021: Cubic and quartic points on modular curves using generalised symmetric Chabauty (arXivLink opens in a new window), joint with Stevan Gajović and Pip Goodman, published in International Mathematics Research Notices.

2021: Computing models for quotients of modular curves (arXivLink opens in a new window), published in Research in Number Theory.

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 (arXivLink opens in a new window), published in Mathematics of Computation.

Other work

2021: Low degree points on modular curves, PhD thesis (pdfLink opens in a new window)

2018: PhD first year report (pdfLink opens in a new window)

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

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  ).

Talks

Slides for the talk I gave in Bristol on May 6, 2020: hereLink opens in a new window.

A video of my online talk at BIRS on September 4, 2020: hereLink opens in a new window.

Lecture notes

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

Contact

E-mail: firstnamelastname *at* msn dot com.