Pseudodifferential Methods and the Mobius Knot Energy

Abstract: The Mobius energy of a knot is a useful analytic tool which can yield information about classical knot invariants. Freedman, He, and Wang proved the existence of curves with a given prime knot type which minimizes the Mobius energy, and they also proved the minimizers are $C^{1,1}$. Shortly after, He proved the minimizers are analytic using nonlocal techniques involving pseudodifferential calculus. I will discuss these methods and how they may apply to unresolved problems regarding the Mobius energy.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology