Knots, Vortices and Reconnection

13^th February 2025, 14:00
Louis H Kauffman
University of Illinois at Chicago, US

Abstract

This talk will discuss a topological model for reconnection of (knotted) vortices and define the reconnection number for a knotted vortex as the least number of reconnections needed to unknot the knot. Using methods of knot cobordism, Khovanov homology and the Rasmussen invariant, we prove that the reconnection number of a positive knot or link is equal to the twice the genus of its Seifert spanning surface. We then generalize these results to virtual knots and links. The talk will discuss these results and open questions, including the physical meaning of Khovanov homology.