Differential Geometry and Topology

course: Singular spectral curves, monopoles, and hyperkaehler metrics

speaker: Roger Bielawski (University of Glasgow)

abstract: In the first talk I will explain the construction of hyperkaehler metrics known as generalised Legendre transform, its relation with flows on Jacobians and how the monopole metrics fit in this scheme. I will also explain what the generalised Legendre transform tells us about the asymptotics of monopole metrics. In the second talk I will explain how to obtain the asymptotic monopole metrics, corresponding to a cluster decomposition of a monopole, from the flows on compactified Jacobians of singular spectral curves. These metrics should be viewed as a deformation of the product of the monopole metrics of lower charges which captures the interaction of the clusters. I will sketch the proof that the rate of approximation of these metrics is exponential in the separation distance of the clusters, and discuss some applications.

timetable:
Tue 28 Sep, 11:15 - 12:15, Sala Conferenze Centro De Giorgi
Wed 29 Sep, 9:45 - 11:15, Sala Conferenze Centro De Giorgi
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