I obtained an ATER (Attaché Temporaire à l'Enseignement et à la Recherche) position at Université Paris-Cité.
I am also a 4th year PhD Student at Sorbonne Université in both PEQUAN and PolSys teams.
I work on fast implementation of polynomial systems solving algorithms with Gröbner bases on GPU, under the supervision of Stef Graillat, Jérémy Berthomieu and Theo Mary.
More precisely, my research has evolved towards the use of floating-point arithmetic for modular matrix multiplication with large finite prime fields.
You may have a look at the proposal for my doctoral research to understand the premises of my research.Likewise, my Master's 2 report describes my early work in the field.
You are invited to look at the latest revision of my article on HAL, I described there a comparison with a Residue Number System approach.
Research
Submitted Articles
Jérémy Berthomieu, Stef Graillat, Dimitri Lesnoff, Theo Mary. Multiword matrix multiplication over large finite fields in floating-point arithmetic. 2026.Reviewed Articles
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ISSAC 2023, Software Presentation (HAL version): Modular matrix multiplication on GPU for polynomial system solving
Conferences
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JNCF 2023: Efficient modular matrix multiplication on GPU for polynomial system solving
Abstract Slides ISSAC 2023: Modular Matrix Multiplication on GPU for Polynomial System Solving
Slides SIAM LA 2024: Multiword Matrix Multiplication over Large Prime Fields on GPUs
Slides LIX Team seminar at X: Multiword matrix decomposition with floating-point representation for modular matrix product
Slides
Softwares
The code associated to the submitted article is available at: https://gitlab.lip6.fr/lesnoff/phdcodeCV
Teaching
Sorbonne Université
- M1 MODEL : Numerical and Symbolic Algorithms Modeling (TD/TME 22-25)
- L1 LU1IN002 : Éléments de Programmation en C (TD 2023)
- L1 LU1IN001 : Algorithmique et Programmation en Python (TD 2023)
- L2 LU2IN006 : Structure de données en C (TME 2024)
GPU programming
If you are interested in GPU programming, you might enjoy reading Programming Massively Parallel Processors: A Hands-on Approach a book by David Kirk, Wen-mei Hwu and Izzat El Hajj. The fifth edition is now available as an ebook on the publisher's website.
I recommend optimizing CUDA kernels on Tensara.org.
To learn how to optimize a matrix multiplication kernel from the ground-up, I found these two blog posts particularly enlightening: