Philippe Michaud-Jacobs
Please note that prior to September 2021 I used the surname Michaud-Rodgers.
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.
- 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).
- 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.
- Mazur's isogeny theorem ( arXivLink opens in a new window ), September 2022.
- 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.
- $\mathbb{Q}$-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.
- On power values of pyramidal numbers, II ( arXivLink opens in a new window ), December 2021 (joint with Andrej Dujella, Kálmán Győry, and Ákos Pintér).
- 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.
- 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).
- 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.
- 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:
- Pinpointing perfect powers: polygons plus pyramids, Warwick Junior Number Theory Seminar, University of Warwick, 31st October 2022, handwritten notesLink opens in a new window.
- 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.
- 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.
- 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.
- 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.
- 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.
- Modular Curves as Moduli Spaces, Modular Forms Study Group, University of Warwick (Online), 5th March 2021, handwritten notesLink opens in a new window.
- 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.
- 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.
- 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
- 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
- Congruent Numbers and Elliptic Curves, WIMP (Warwick-Imperial) Autumn 2019 Conference, University of Warwick, 30th November 2019, handwritten notesLink opens in a new window.
- 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.
- Sums of Three Squares, WIMP (Warwick-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019, slidesLink opens in a new window.
- 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:
- COUNT, COmputations and their Uses in Number TheoryLink opens in a new window, CIRM, Marseille, France, 27th February - 3rd March 2023.
- Modern Breakthroughs in Diophantine ProblemsLink opens in a new window, Banff, Canada, 19th - 24th June 2022.
- Rational Points 2022Link opens in a new window, Lichtenfels, Germany, 27th March - 2nd April 2022.
- Modular Curves WorkshopLink opens in a new window, MIT (Online), 21st - 25th March 2022.
- Young Researchers in Algebraic Number TheoryLink opens in a new window (YRANT), 3rd edition, University of Bristol (Online), 18th - 20th August 2021.
- Young Researchers in MathematicsLink opens in a new window, 10th edition, University of Bristol (Online), 7th - 9th June 2021.
- Modern Breakthroughs in Diophantine ProblemsLink opens in a new window, BIRS Online, 31st August - 4th September 2020.
- Warwick Number Theory SeminarLink opens in a new window, University of Warwick / Online, 2019-2022,
- ROWLink opens in a new window (Reading-Oxford-Warwick) Diophantine Geometry Seminar, Online, 2020-2021.
- WIMPLink opens in a new window (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 SchoolLink opens in a new window, University of Glasgow, 16th - 27th July 2018.
Other Mathematical Writing:
- Quadratic Points on Non-Split Cartan Modular Curves ( PDFLink opens in a new window ), first-year PhD project supervised by Professor Samir Siksek and Dr Damiano Testa, September 2020.
- Magic Squares of Squares ( PDFLink opens in a new window ), fourth-year undergraduate project supervised by Dr Damiano Testa, April 2019.
- Quadratic Forms and the Three-Square Theorem ( PDFLink opens in a new window ), third-year undergraduate essay supervised by Professor John Cremona, April 2018.
- Oddly Perfect ( PDFLink opens in a new window ), second-year undergraduate essay, March 2017.