Dia: Dimecres 1 d'octubre de 2025
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Robert Cardona, Universitat de Barcelona
Títol: Beyond helicity: dynamical invariants of 3D volume-preserving flows and a conjecture of Arnold and Khesin
Resum: Volume-preserving flows on 3-manifolds arise naturally in fluid dynamics and plasma physics, where the vorticity or magnetic field is transported by the motion of the fluid. A central role is played by the helicity, a classical invariant introduced by Woltjer and Moffatt that measures the average linking of flow lines. Helicity is the best-known “coadjoint invariant” of a volume-preserving flow, which implies that it is preserved under the natural symmetries of the fluid equations, and it enjoys important uniqueness properties among such invariants. In this talk, which is meant to be accessible, I will first explain and motivate the relevant notions, and then focus on the question of how far the uniqueness of helicity really goes. In particular, I will show that the Ruelle invariant is, in a precise sense, everywhere independent of helicity in the 𝒞 ¹-topology. This gives a strong negative answer to the 𝒞 ¹-case of a conjecture of Arnold and Khesin.
This is joint work with Julian Chaidez (University of Southern California) and Francisco Torres de Lizaur (Universidad de Sevilla).
Last updated: Mon Sep 29 18:31:58 2025