### Speaker

Maxime Breden
(Ecole Polytechnique, CMAP)

### Description

I will present some techniques that can be used to “turn a numerical simulation into a theorem”. More precisely, the goal is to use a fixed point argument in the neighborhood of an approximate solution which has been obtained numerically, in order to prove the existence of a true solution nearby, and to also get guaranteed and fully computable a posteriori error estimates between this true solution and the numerical approximation. As an example, I will discuss some recent results about traveling waves in the so-called DPCM model, obtained in collaboration with C. Chainais-Hillairet and A. Zurek.