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Mathematics Institute

Philippe Michaud-Jacobs

Please note that prior to September 2021 I used the surname Michaud-Rodgers.Me and my dog

I am a fourth-year PhD student in number theory under the supervision of Professor Samir Siksek and Dr Damiano TestaLink opens in a new window. Previously, I completed my MMath degree at the University of Warwick.

Email: p dot rodgers at warwick dot ac dot uk (this email is indeed correct despite the name not matching).

Research Interests:

My research is focused on the explicit resolution of Diophantine equations, the study of low-degree points on modular curves, and how the two interact. More generally, I am interested in computational number theory and arithmetic geometry.

Papers and Preprints:

My arXiv author identifier is http://arxiv.org/a/michaudjacobs_p_1Link opens in a new window.

My ORCID iD is https://orcid.org/0000-0001-9415-8519Link opens in a new window.

Any code associated with the following papers is available on my GitHub page: https://github.com/michaud-jacobsLink opens in a new window.

  1. Computing quadratic points on modular curves $X_0(N)$ ( arXivLink opens in a new window ), March 2023 (joint with Nikola Adžaga, Timo Keller, Filip Najman, Ekin Ozman, and Borna Vukorepa).
  2. Computing points on bielliptic modular curves over fixed quadratic fields ( arXivLink opens in a new window ), January 2023, to appear in Bulletin of the Australian Mathematical Society.
  3. Mazur's isogeny theorem ( arXivLink opens in a new window ), September 2022.
  4. On elliptic curves with $p$-isogenies over quadratic fields ( online versionLink opens in a new window, open access ) ( arXivLink opens in a new window ), June 2022, published online in Canadian Journal of Mathematics.
  5. $\mathbb{Q}$-curves and the Lebesgue–Nagell equation ( arXivLink opens in a new window ), February 2022 (joint with Michael A. Bennett and Samir Siksek), to appear in Journal de Théorie des Nombres de Bordeaux.
  6. On power values of pyramidal numbers, II ( arXivLink opens in a new window ), December 2021 (joint with Andrej Dujella, Kálmán Győry, and Ákos Pintér).
  7. On some generalized Fermat equations of the form $x^2 + y^{2n} = z^p$ ( published versionLink opens in a new window, open access ) ( arXivLink opens in a new window ), Mathematika 68 (2022), no 2, 344-361.
  8. A unique perfect power decagonal number ( published versionLink opens in a new window, open access ) ( arXivLink opens in a new window ), Bulletin of the Australian Mathematical Society 105 (2022), no. 2, 212-216 (published under the name Michaud-Rodgers).
  9. Fermat's Last Theorem and modular curves over real quadratic fields ( published versionLink opens in a new window ) ( arXivLink opens in a new window ), Acta Arithmetica 203 (2022), no. 4, 319-352.
  10. Quadratic points on non-split Cartan modular curves ( published versionLink opens in a new window ) ( arXivLink opens in a new window ), International Journal of Number Theory 18 (2022), no. 2, 245-267 (published under the name Michaud-Rodgers).

Talks:

  1. Pinpointing perfect powers: polygons plus pyramids, Warwick Junior Number Theory Seminar, University of Warwick, 31st October 2022, handwritten notesLink opens in a new window.
  2. On some generalized Fermat equations of the form $x^2 + y^{2n} = z^p$, Modern Breakthroughs in Diophantine Problems, Banff, Canada, 20th June 2022, slidesLink opens in a new window and compressed slidesLink opens in a new window, videoLink opens in a new window.
  3. Rational isogenies of prime degree, Triangle Groups, Belyi Uniformization, and Modularity, Bhaskaracharya Pratishthana (Online), 7th April 2022, slidesLink opens in a new window and compressed slidesLink opens in a new window, videoLink opens in a new window.
  4. A Unique Perfect Power Decagonal Number, Young Researchers in Algebraic Number Theory (YRANT), 3rd edition, University of Bristol (Online), 20th August 2021, slidesLink opens in a new window and compressed slidesLink opens in a new window.
  5. Fermat's Last Theorem – Not Enough Margin! Young Researchers in Mathematics, 10th edition, University of Bristol (Online), 8th June 2021, slidesLink opens in a new window and compressed slidesLink opens in a new window.
  6. Fermat's Last Theorem and Modular Curves over Real Quadratic Fields, Seminar on Number Theory and Algebra, University of Zagreb (Online), 17th May 2021, slidesLink opens in a new window and compressed slidesLink opens in a new window.
  7. Modular Curves as Moduli Spaces, Modular Forms Study Group, University of Warwick (Online), 5th March 2021, handwritten notesLink opens in a new window.
  8. Fermat's Last Theorem Over Totally Real Fields, London Junior Number Theory Seminar (Online), 16th February 2021, slidesLink opens in a new window and compressed slidesLink opens in a new window.
  9. Who Wants to Be a Millionaire? (The Hard Way), Warwick Maths Society Talks Series, University of Warwick (Online), 1st December 2020, slidesLink opens in a new window and compressed slidesLink opens in a new window, videoLink opens in a new window.
  10. Global Class Field Theory: Classical Approach, Class Field Theory Study Group, University of Warwick (Online), 20th November 2020, handwritten notes.Link opens in a new window
  11. Fermat's Last Theorem and the Modular Method, Warwick Postgraduate Seminar (Online), 4th November 2020, slidesLink opens in a new window and compressed slides.Link opens in a new window
  12. Congruent Numbers and Elliptic Curves, WIMP (Warwick-Imperial) Autumn 2019 Conference, University of Warwick, 30th November 2019, handwritten notesLink opens in a new window.
  13. Formalism of Period Rings and $B_{HT}$, $p$-adic Hodge Theory study group, University of Warwick, 15th November 2019, handwritten notesLink opens in a new window.
  14. Sums of Three Squares, WIMP (Warwick-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019, slidesLink opens in a new window.
  15. Magic Squares of Squares, Warwick Maths Society Talks Series, University of Warwick, 26th February 2019, slidesLink opens in a new window.

Teaching and Other Responsibilities:

  • Associate Fellow of the Higher Education Academy, 2022.
  • Reviewer for Mathematical Reviews ( linkLink opens in a new window ), 2022.
  • Referee for Research in Number Theory (x 2), 2021 and 2022.
  • Referee for Mathematics of Computation, 2022.
  • Teaching assistant (online) for the second-year module Introduction to Number Theory (MA257), Term 2, 2022.
  • Analysis 1 class teacher, Term 1, 2021.
  • Referee for Journal of Number Theory, 2021.
  • Exam marking (online) for the third-year module Galois Theory (MA3D5), approx. 160 questions, Term 3, 2021.
  • Video transcript editing for the first-year module Linear Algebra (MA106), approx. 8 hours of video, April 2021.
  • Teaching assistant (online) for the third-year module Galois Theory (MA3D5), Term 2, 2021.
  • Supervisor (online) to first-year maths and philosophy undergraduates, Terms 1 and 2, 2020-2021.
  • Teaching assistant (online) for the third-year module 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.

Conferences, Seminars, and Summer Schools Attended:

Other Mathematical Writing: