Conservation of Writhe Helicity Under Anti-Parallel Reconnection

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to site-specific recombination in DNA. The helicity of a collection of flux tubes can be calculated in terms of writhe, twist and linking among tubes. We prove that the writhe helicity is conserved under anti-parallel reconnection [1]. We will discuss the mathematical similarities between reconnection events in biology and physics, and the relationship between iterated reconnection and curve topology. We will discuss helicity and reonnection in a tangle of confined vortex circles in a superfluid. Support from a Simons Foundation Collaboration Grant for Mathematicians is gratefully acknowledged. [1] Laing C.E., Ricca R.L. {\&} Sumners D.W. (2015) Conservation of writhe helicity under anti-parallel reconnection, Nature Scientific Reports 5:9224 \textbar DOI: 10.1038/srep09224.