# Philippe Michaud-Rodgers

I am a second-year PhD student in number theory under the supervision of Professor Samir Siksek and Dr Damiano Testa. I am especially interested in the study of Diophantine equations.

I am currently studying ternary Diophantine equations using modularity. In particular, I am working on Fermat's Last Theorem over totally real fields, but I feel this webpage is too small to explain my truly remarkable research on this problem.

During the first year of my PhD I studied quadratic points on some non-split Cartan modular curves. This led to proving that certain classes of elliptic curves over quadratic fields are modular. Here is a link to the project:* First-Year Project*. Following this, I wrote a paper on my findings (see below).

Previously, I completed my MMath degree at the University of Warwick. My final year project, supervised by Dr Damiano Testa, was titled *Magic Squares of Squares* and used techniques from algebraic geometry to study the open question of whether there exists a magic square consisting of nine distinct square integer entries.

Email: p dot rodgers at warwick dot ac dot uk

**Papers and Preprints:**

- Quadratic Points on Non-Split Cartan Modular Curves ( arXiv ), submitted to Mathematics of Computation.

**Talks Given:**

- Global Class Field Theory: Classical Approach, Class Field Theory Study Group, University of Warwick (Online), 20th November 2020, handwritten notes;
- Fermat's Last Theorem and the Modular Method, Warwick Postgraduate Seminar (Online), 4th November 2020, Slides and compressed slides;
- Congruent Numbers and Elliptic Curves, WIMP (Warwick-Imperial) Autumn 2019 Conference, University of Warwick, 30th November 2019;
- Formalism of Period Rings and $B_{HT}$, $p$-adic Hodge Theory study group, University of Warwick, 15th November 2019;
- Sums of Three Squares, WIMP (Warwick-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019;
- Magic Squares of Squares, Warwick Maths Society Talks Series, University of Warwick, 26th February 2019.

**Conferences, Seminars, and Summer Schools Attended:**

- Modern Breakthroughs in Diophantine Problems, BIRS Online, 31st August - 4th September 2020;
- Warwick Number Theory Seminar, University of Warwick / Online, 2019-2020;
- ROW (Reading-Oxford-Warwick) Diophantine Geometry Seminar, Online, 2020;
- WIMP (Warwick-Imperial) Autumn 2019 Conference, University of Warwick, 30th November 2019;
- WIMP (Warwick-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019;
- London Mathematical Society Undergraduate Research School, University of Glasgow, 16th - 27th July, 2018.

**Teaching:**

- Supervisor (online) to first-year maths and philosophy undergraduates, Term 1 - Ongoing 2020;
- Teaching Assistant (online) for Algebraic Number Theory (MA3A6), Term 1 2020;
- Supervisor to first-year maths undergraduates, Terms 1 and 2, 2018-2019;
- Analysis I Class Helper, Term 1 2016 and Term 1 2017.