EVENT DETAILS AND ABSTRACT

Title: Helicity and linking numbers for Anosov flows
Speaker: Solly Coles
Speaker Info:
Brief Description:
Special Note: Chicago Action Now
Abstract:

Helicity is an invariant of volume-preserving flows in 3-dimensional space, useful for solving variational problems in hydrodynamics. Shortly after its introduction, H. K. Moffatt noticed a connection between helicity and the knottedness of flow trajectories. This connection was developed by V. Arnold and T. Vogel, who showed that for flows on homology spheres, helicity can be obtained in terms of linking numbers of knots made by closing flow trajectories with geodesic arcs. In this talk I will discuss recent work (joint with R. Sharp) where we consider Anosov flows on homology spheres, and characterise helicity in terms of the linking numbers of periodic orbits.