Welcome!
I am a post-doctoral researcher at the University of Calgary, working with Renate Scheidler. I defended my PhD thesis in September of 2024, under the direction of Emmanuel Thomé and Pierre-Jean Spaenlehauer. I am interested in the algorithmics of Drinfeld modules and their applications to computer algebra and cryptography. I also studied musicology and in mechanics!
Drinfeld modules
Drinfeld modules were introduced in the 1970s by Vladimir Drinfeld. They serve multiple purposes, all related to describing function fields. On the one hand, rank 1 Drinfeld modules over Fq(T) generate cyclotomic function fields. On the other hand, rank 2 Drinfeld modules over (but not restrected to) a finite field provide an analogue of the theory of complex multiplication. Drinfeld modules exist with arbitrary ranks, and after that, generalizations include abelian A-modules, or even shtukas…
Research summary
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My first interest lied in computing an important group action from the class field theory of function fields: the class group of the endomorphism ring of an ordinary rank 2 Drinfeld module over a finite field acts faithfully and transitively on a set of isomorphism classes of Drinfeld modules. This is an analogue of the action Couveignes-Rostovtsev-Stolbunov used in post-quantum isogeny-based cryptography. In our context, we show that the class group is isomorphic to the Picard group of an imaginary hyperelliptic curve, which allows our algorithm to run in about 20 ms. This joint-work with Pierre-Jean Spaenlehauer was accepted at the Journal of Symbolic computation.
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I also collaborated with Xavier Caruso on the computation of Drinfeld module isogeny norms and endomorphism characteristic polynomials. Our algorithms rely on a correspondence between Drinfeld modules and Anderson motives. This insight allows to reduce our problems to standard linear algebra computations, and to create algorithms that are competitive, while also working on any function ring and rank. Our paper is to appear in Mathematics of Computation.
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With a Mitacs Globalink Research grant (6k CAD) and a Lorraine University grant (6.5k EUR) I was fortunate to visit Renate Scheidler at the University of Calgary for three months. We collaborated on various topics in the algorithmics of Drinfeld modules, with a main focus (with Gaetan Bisson) towards different approaches to the computation of their endomorphism ring.
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This days, I am in the process of finishing co-writing a survey on a computational approach to Drinfeld modules. For the research, I’m also focusing on the computation of torsion spaces of Drinfeld modules; apart from the algorithm, I’m exploring new ways of seeing classical results related to the correspondence between Drinfeld modules and Anderson motives.
Software
I co-wrote the first implementation of Drinfeld modules in the standard distribution of SageMath (joint work with David Ayotte, Xavier Caruso and Joseph Musleh)! Our contribution was merged with version 10.0, and our software presentation was published at ISSAC 2023!. More details here!
Ethics
I wish to contribute to cryptography, which I believe is the cornerstone of numerous human rights. Generally, I want my work to be meaningful, well-crafted, and most of all, helpful.