Mathematical colloquium “Computer assisted theorems in dynamical systems”

The talk is given by Prof. Jan Bouwe van den Berg (VU Amsterdam, Department of Mathematics).

Abstract

In nonlinear analysis we often simulate dynamics on a computer, or calculate a numerical solution to a partial differential equation. This gives very detailed, stimulating information. However, it would be even better if we can be sure that what we see on the screen genuinely represents a solution of the problem. In particular, rigorous validation of the computations would allow such objects to be used as ingredients of theorems. The past few decades have seen enormous advances in the development of computer assisted proofs in dynamics. Attention is now turning to infinite dimensional nonlinear dynamics generated by PDEs, integral equations, delay equations, and infinite dimensional maps. In this talk we will review recent developments, such as connecting orbit problems in pattern formation, as well as applications in the setting of spatio-temporal periodicity.