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Hyperbolic & Dispersive PDE Seminar

Daniel Eceizabarrena -- Multifractality in the evolution of vortex filaments

Daniel Eceizabarrena (University of Massachusetts Amherst)

Location:  Hill 705
Date & time: Thursday, 09 May 2024 at 3:50PM - 4:50PM

Vortex 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


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 x0 = 0. I will highlight how the analysis seems to critically depend on x0, 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 in collaboration with Valeria Banica (Sorbonne Universite), Andrea Nahmod (University of Massachusetts) and Luis Vega (BCAM, UPV/EHU).

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