Title: Computers and mathematics in PDE: new developments and challenges

Speaker: Javier Gómez-Serrano

Abstract: In the last 50 years computing power has experienced an enormous development: from Moore’s law — every two years the number of transistors doubled — up to the latest developments in GPUs. In this talk I will address the interaction between traditional and modern mathematics and how computers have helped over the last decade providing rigorous proofs in the context of PDE. I will also describe new exciting future directions in the field, in particular addressing the incoming new revolution from the interaction of machine learning and mathematics.

The first part will cover general background, with an emphasis in computer-assisted proofs and the machine-learning ingredients.
The second part will explain how to combine those ingredients with classical analysis to prove mathematical theorems, in particular instances.