Gilles Villard

Gilles Villard is a Researcher at the CNRS, affiliated with the Pascaline project-team and the Laboratoire LIP (a joint unit with CNRS, ENS Lyon, INRIA, Université Claude Bernard Lyon 1, and the University of Lyon). His research activities focus on exact linear algebra, lattice basis reduction, and computational complexity, with contributions to symbolic computation, polynomial algorithms, and high-performance algebraic computing.

He teaches advanced courses in symbolic summation and integration at the Master’s level (M2) at École Normale Supérieure de Lyon. His work emphasizes structured matrix computations, including quasiseparable matrices and Sylvester matrices, and integrates theoretical advancements with practical software development, such as the mapml library interfacing Maple with the pml C++ library and the hplll library for lattice problems.

Villard has organized and contributed to major international conferences, including ISSAC, STACS, and the Springer TMSC volume for the Recent Trends in Computer Algebra (RTCA) initiative. His articles frequently explore topics like Krylov subspace methods, resultant computation, and modular composition, emphasizing algorithmic efficiency and numerical stability.

He has been involved in collaborative projects like the LinBox joint CNRS/NSF initiative and the FLINT library development, and maintains active participation in research networks such as the GdR CNRS Informatique Fondamentale et ses Mathématiques and the International Linear Algebra Society (ILAS).