Daniel Eceizabarrena (BCAM)

Multifractality in the evolution of vortex filaments.

Vortex filaments that evolve according to the binormal flow are expected to exhibit turbulent properties. Aiming to quantify this, I will discuss the multifractal properties of Riemann's non-differentiable function, a generalization of which approximates the evolution of regular polygonal vortex filaments. I will highlight how the analysis strongly depends on Gauss sums, a restricted version of Diophantine approximation, the Duffin Schaeffer theorem and the mass transference principle. This talk is based on the article https://doi.org/10.1007/s00208-024-02971-0 in collaboration with Valeria Banica, Andrea R. Nahmod and Luis Vega.