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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.