Philippe Michaud-Jacobs

I am now working outside academia as a software engineer ().

I submitted my PhD thesis ( ) in September 2023 and passed my viva in December 2023.

I will continue to keep this page up to date (for article publications) while I still have access to it.

If you wish to contact me and my 果冻传媒 email no longer works, then you may use my personal email address which you can construct as:

"Initial of first name" + "." + "first part of surname without hyphen" + "initial of second part of surname" + "@gmail.com"

I was a PhD student in number theory (2019 – 2023) under the supervision of and . Previously, I completed my MMath degree at the 果冻传媒.

Me and my dog

Please note that prior to September 2021 I used the surname Michaud-Rodgers.

Email: p dot rodgers at warwick dot ac dot uk (this email is correct despite the name not matching, and it will be monitored until it is terminated).

My Erd枚s number is 2!

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:

My arXiv author identifier is .

My ORCID iD is .

Any code associated with the following papers is available on my GitHub page: . Links to the specific repositories are available hereLink opens in a new window.

Quadratic points on $X_0(163)$ ( ) ( ) (joint with Filip Najman), Journal of Algebra, 666 (2024), no. 1, 279-288.
Computing quadratic points on modular curves $X_0(N)$ ( ) ( ) (joint with Nikola Ad啪aga, Timo Keller, Filip Najman, Ekin Ozman, and Borna Vukorepa), Mathematics of Computation, 93 (2024), no. 347, 1371-1397.
Computing points on bielliptic modular curves over fixed quadratic fields ( , open access ) ( ), Bulletin of the Australian Mathematical Society, 109 (2024), no. 1, 6-13.
Mazur's isogeny theorem ( ), 2022, to appear in Proceedings of The Year-Long Program on Triangle Groups, Belyi Uniformization, and Modularity: IInd Trimester Proceedings, Bhaskaracharya Pratishthana, Pune, India ().
On elliptic curves with $p$-isogenies over quadratic fields ( , open access ) ( ), Canadian Journal of Mathematics 75 (2023), no. 3, 945-964.
$\mathbb{Q}$-curves and the Lebesgue–Nagell equation ( , open access) ( ) (joint with Michael A. Bennett and Samir Siksek), Journal de Th茅orie des Nombres de Bordeaux 35 (2023), no. 2, 495-510.
On power values of pyramidal numbers, II ( ) ( ) (joint with Andrej Dujella, K谩lm谩n Gy艖ry, and 脕kos Pint茅r), Acta Arithmetica 208 (2023), no. 3, 199-213.
On some generalized Fermat equations of the form $x^2 + y^{2n} = z^p$ ( , open access ) ( ), Mathematika 68 (2022), no. 2, 344-361.
A unique perfect power decagonal number ( , open access ) ( ), 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 ( ) ( ), Acta Arithmetica 203 (2022), no. 4, 319-352.
Quadratic points on non-split Cartan modular curves ( ) ( ), International Journal of Number Theory 18 (2022), no. 2, 245-267 (published under the name Michaud-Rodgers).

Talks:

Sieving for quadratic points on bielliptic curves, Representation Theory XVIII (Number theory section), Dubrovnik, Croatia, 19th June 2023, slidesLink opens in a new window and compressed slidesLink opens in a new window.
Isogenies of elliptic curves and Diophantine equations, Number Theory Seminar, University of Manchester, 9th May 2023, slidesLink opens in a new window and compressed slidesLink opens in a new window.
Isogenies of elliptic curves and Diophantine equations, Seminar on Algebra and Number Theory, University of Zagreb, 3rd May 2023, slidesLink opens in a new window and compressed slidesLink opens in a new window.
Pinpointing perfect powers: polygons plus pyramids, 果冻传媒 Junior Number Theory Seminar, 果冻传媒, 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, .
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, .
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 果冻传媒 Group, 果冻传媒 (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), 果冻传媒 Maths Society Talks Series, 果冻传媒 (Online), 1st December 2020, slidesLink opens in a new window and compressed slidesLink opens in a new window, .
Global Class Field Theory: Classical Approach, Class Field Theory 果冻传媒 Group, 果冻传媒 (Online), 20th November 2020, handwritten notes.Link opens in a new window
Fermat's Last Theorem and the Modular Method, 果冻传媒 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 (果冻传媒-Imperial) Autumn 2019 Conference, 果冻传媒, 30th November 2019, handwritten notesLink opens in a new window.
Formalism of Period Rings and $B_{HT}$, $p$-adic Hodge Theory study group, 果冻传媒, 15th November 2019, handwritten notesLink opens in a new window.
Sums of Three Squares, WIMP (果冻传媒-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019, slidesLink opens in a new window.
Magic Squares of Squares, 果冻传媒 Maths Society Talks Series, 果冻传媒, 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 ( ), 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:

(Number theory section), Dubrovnik, Croatia, 18th - 24th June 2023.
, CIRM, Marseille, France, 27th February - 3rd March 2023.
, Banff, Canada, 19th - 24th June 2022.
, Lichtenfels, Germany, 27th March - 2nd April 2022.
, MIT (online), 21st - 25th March 2022.
(YRANT), 3rd edition, University of Bristol (online), 18th - 20th August 2021.
, 10th edition, University of Bristol (online), 7th - 9th June 2021.
, BIRS Online, 31st August - 4th September 2020.
(Reading-Oxford-果冻传媒) Diophantine Geometry Seminar, online, 2020-2021.
果冻传媒 Number Theory SeminarLink opens in a new window, 果冻传媒 / online, 2019-2023,
WIMPLink opens in a new window (果冻传媒-Imperial) Autumn 2019 Conference, 果冻传媒, 30th November 2019.
WIMP (果冻传媒-Imperial) Spring 2019 Conference, Imperial College London, 9th March 2019.
, University of Glasgow, 16th - 27th July 2018.

Other Mathematical Writing:

Diophantine Equations and Modular Curves ( ), PhD thesis supervised by Professor Samir Siksek and Dr Damiano Testa, September 2023.
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.