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 and Pierre Lairez. Validated numerics for algebraic path tracking. Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation, 36–45. July 2024. [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 Pierre Lairez.
   algpath is a proof-of-concept Rust package for the rigorous computation of the continuation of a regular zero of a polynomial when changing a parameter.
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 Nationales de Calcul Formel (JNCF), CIRM, March 2024. [slides]
2. Numerical Safety for Computer-Aided Proofs (NUSCAP), LIP6, May 2024. [slides]
3. International Symposium on Symbolic and Algebraic Computation (ISSAC), NC State University, July 2024. [slides]

Teaching

1. MAA101 - Linear Algebra (teaching assistant), École polytechnique, fall 2023.