RIEMANN’S NON-DIFFERENTIABLE FUNCTION AND THE BINORMAL CURVATURE FLOW ( Joint work with Valeria Banica)
Speaker:
Luis Vega, La Universidad del País Vasco
Date and Time:
Thursday, November 5, 2020 - 9:00am to 9:45am
Location:
Online
Abstract:
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.