Joint BCAM-UPV/EHU Analysis and PDE seminar: Riemann's Non-differentiable function and the binormal curvature flow

Date: Thu, Feb 11 2021

Hour: 12:00

Speakers: Luis Vega

We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious non- linear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.

This is a joint work with Valeria Banica.

Link to the session:

More info at




Confirmed speakers:

 Luis Vega