Seminar| Institute of Mathematical Sciences
Time: Wednesday, Feburary 26th, 2025,14:00-15:00
Location: IMS, RS408
Speaker:Daniel Eceizabarrena, BCAM, Spain
Abstract:BVortex filaments that evolve according the binormal flow are expected to exhibit turbulent properties. Aiming to quantify this, I will discuss the multifractal properties of the family of functions \[ R_{x_0}(t) = \sum_{n \neq 0} \frac{e^{2\pi i ( n^2 t + n x_0 ) } }{n^2}, x_0 \in [0,1],\] that approximate the trajectories of regular polygonal vortex filaments. These functions are a generalization of the classical Riemann's non-differentiable function, which we recover when $x_0 = 0$. I will highlight how the analysis seems to critically depend on $x_0$, and I will discuss the important role played by 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 (Sorbonne Universit\'e), Andrea Nahmod (University of Massachusetts) and Luis Vega (BCAM, UPV/EHU).