About me

I am a PhD student in the team Mathexp. My thesis is supervised by Pierre Lairez. I mainly focus on computer algebra, effective algebraic geometry and topology.

Research

Articles

1. Alexandre Guillemot. Certified Algebraic Path Tracking with Algpath. 2025. To appear. [hal][pdf] Issac '25 distinguished software presentation!
   Algpath is a certified homotopy continuation software. We upgrade the previous fixed-precision Rust implementation by incorporating mixed, adaptive precision with minimal overhead. This allows us to tackle problems on which the initial implementation fails due to the inability to increase precision, and where uncertified methods may fail or path jump.
2. Alexandre Guillemot and Pierre Lairez. Validated numerics for algebraic path tracking. Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation, 36–45. July 2024. [hal][doi][arxiv][pdf]
   Using validated numerical methods, interval arithmetic and Taylor models, we propose a certified predictor-corrector loop for tracking zeros of polynomial systems with a parameter. We provide a Rust implementation which shows tremendous improvement over existing software for certified path tracking.

Software

1. algpath. Implementation by Alexandre Guillemot and Pierre Lairez.
   algpath is a Rust package for the rigorous computation of the continuation of a regular zero of a parametrized polynomial system as the parameter varies.
2. algpath bench. Implementation by Alexandre Guillemot and Pierre Lairez.
   algpath bench is a repository for homotopy continuation benchmarking. It is able to test different packages on polynomial systems, and to process the results in the form of tables and latex output.

Talks

1. Journées de géométrie algorithmique (Jga), station biologique de Roscoff, October 2025. [slides]
2. Pascaline seminar, LIP, ENS Lyon, September 2025. [slides]
3. International Symposium on Symbolic and Algebraic Computation (ISSAC), Center for Research in Mathematics (CIMAT), July-August 2025. [slides]
4. Applications of Computer Algebra (ACA), Cultural Conference Center of Heraklion, July 2025. [slides]
5. SIAM Conference on Applied Algebraic Geometry (AG), University of Wisconsin Madison, July 2025. [slides]
6. Séminaire AG, LMV, May 2025. [slides]
7. Journées Nationales de Calcul Formel (JNCF), CIRM, March 2025. [slides]
8. International Symposium on Symbolic and Algebraic Computation (ISSAC), NC State University, July 2024. [slides]
9. Numerical Safety for Computer-Aided Proofs (NUSCAP), LIP6, May 2024. [slides]
10. Journées Nationales de Calcul Formel (JNCF), CIRM, March 2024. [slides]

Teaching

1. CSC_41011_EP - Les bases de la programmation et de l'algorithmique (teaching assistant, two groups), École polytechnique, fall 2025.
2. CSC_1S002_EP - Computer Programming (teaching assistant, one group), École polytechnique, summe 2024.
3. CSC_41011_EP - Les bases de la programmation et de l'algorithmique (teaching assistant, two groups), École polytechnique, fall 2024.
4. MAA101 - Linear Algebra (teaching assistant, two groups), École polytechnique, fall 2023.