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**Luis Vega González**

- His research is mainly focused in the interplay of Fourier Analysis and Partial Differential Equations of Mathematical Physics.
- More recently he has been interested in the deep connection between uncertainty principles, that are easily described using the Fourier transform, and lower bounds for solutions of linear and non-linear dispersive equations. A consequence of these estimates from below is that compact perturbations of a solitary wave or soliton instantaneously destroys its exponential decay.
- Another one of his recent interests is on fluid mechanics and turbulence. More concretely in the so called Localized Induction Approximation for the evolution of vortex filaments and the relevance of the presence of corners in the filament. The results concerning regular polygons seem to me quite striking.
- Finally, he has been also working on relativistic and non-relativistic equations with singular electromagnetic potentials. The singularities of the potentials are critical from the point of view of the scaling symmetry.

Personal webpage:

http://www.bcamath.org/en/people/lvega

**Plenary talk**: **The Vortex Filament Equation for regular polygons**

I shall present some recent work done in collaboration with F. De la Hoz about the evolution of regular polygons within the so-called Vortex Filament Equation. Each corner of the polygon generates some Kelvin waves that interact in a non-linear way that is closely related to the (linear) Talbot effect in optics. The question of the connection between the Talbot effect and turbulence will be also addressed, and in particular the appearance of multi-fractals and their relation with Frisch-Parisi conjecture.

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