CERMICS/ENPC | France
Jean-François Pommaret is a French mathematician and mathematical physicist, now Emeritus Researcher at École des Ponts ParisTech (CERMICS), whose work bridges differential geometry, partial differential equations, algebraic analysis, and gauge / gravity theory. He graduated from École Polytechnique and the École Nationale des Ponts et Chaussées (X64) and obtained further training in mathematics and theoretical physics (Paris VI). His research interests include the formal theory of partial differential equations, Lie pseudogroups, differential sequences (Janet, Spencer), homological algebra, differential modules, gauge theory, and the mathematical foundations of general relativity and gravitational waves. In particular, he has advanced the idea that the Einstein equations cannot be parametrized analogously to Maxwell’s equations, and he applies double duality and extension modules in differential homological algebra to reexamine the structure of the Riemann, Ricci, and Weyl tensors in various dimensions. His contributions also revisit classical elasticity (Cosserat theory), conformal geometry, and the interplay of gauge theory and gravitation. Throughout his career, he has promoted computational and algorithmic approaches (e.g. via Pommaret bases) to problems in differential algebra and mathematical physics. He is known for provocative claims about the (non)existence of gravitational waves from a rigorous mathematical standpoint, prompting debate and further study in the mathematical physics community.
Featured Publications
Pommaret, J.-F. (2025, September 30). Differential Galois theory and Hopf algebras for Lie pseudogroups. Axioms, 14(10), 729.
Pommaret, J.-F. (2025, September 24). Electromagnetism and gravitation: A conformal jigsaw puzzle. Journal of Modern Physics.
Pommaret, J.-F. (2025, March). Why black holes cannot exist? Open Access Government.
Pommaret, J.-F. (2025, March 26). From differential sequences to black holes. Journal of Modern Physics.
Pommaret, J.-F. (2024, December). From computer algebra to gravitational waves. Journal of Applied Mathematics,