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Magnetic helicity is an ideal MHD invariant; it measures geometric and topological properties of a magnetic field. The talk will begin by reviewing helicity and its mathematical properties. It can be decomposed in several ways (for example, self and mutual helicity, Fourier spectra, fieldline helicity, linking, twist, and writhe). The talk will also review methods of measuring helicity flux, as well as applications in solar and stellar astrophysics.
The poloidal-toroidal decomposition of a vector field will be discussed, with a generalization to arbitrary geometries. I will then discuss some new developments in measuring localized concentrations of helicity in a well-defined, gauge invariant manner, using wavelets.