### Speaker: Roberto Capistrano-Filho

### Universidade Federal de Pernambuco – Brasil

### Date: Tuesday, October 10th, 2023 at 12 Santiago time

**Abstract:**In 93′ Jean Bourgain discovered a subtle smoothing property of solutions of the KdV equation posed on a periodic domain. Since this celebrated article, the smoothing properties for dispersive systems are now well known. In this talk, we will see that in the last 15 years, the Bourgain spaces are fundamental to addressing the global control problems in periodic frameworks. Precisely, we will show that the propagation of compactness and regularity have been observed thanks to these spaces in various control problems for dispersive systems.

**Venue:** Sala John Von Neumann, 7th floor, Beauchef 851 / Online via Zoom

**Chair:** Rayssa Caju