PhD Opening 2026 with ​Maxime Breden

14.15
Welcome
Willem Adriaan De Graaf (PhD Coordinator)

14.30
Maxime Breden
Department of Applied Mathematics, Ecole Polytechnique
​"​An introduction to computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem"
  
Abstract:
The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear ODEs or PDEs, based on numerical simulations. The general strategy consists in combining a priori and a posteriori error estimates, interval arithmetic, and a fixed point theorem applied to a quasi-Newton operator. Starting from a numerically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neighborhood of the numerical approximation.
I will first present the main ideas behind these techniques on a simple example, then describe a rather general framework in which they can be applied, and finally, time permitting, discuss some applications in fluid dynamics or population dynamics.

​15.45
Small Break

16.00
XLI cycle Phd Students Presentation