L^2 Geometry of Hyperbolic Monopoles

This lecture by Derek Harland from Leeds University explores the L^2 geometry of hyperbolic monopoles. Discover how Harland presents a new solution to the problem of ill-defined metrics for monopoles on hyperbolic space, which involves a divergent integral. Learn about Nick Manton's 1982 discovery of a metric whose geodesics approximate the dynamics of slowly-moving monopoles, and how these hyperkähler metrics have reappeared across various physical and mathematical contexts. The presentation introduces a gauge-fixing condition arising from supersymmetry that leads to a hyperbolic analogue of the hyperkähler geometry of Euclidean monopoles.