Monopoles and the Sen Conjecture
- Date: Wednesday 22 February 2017, 15:00 – 16:30
- Location: Roger Stevens LT 12 (10M.12)
- Type: Geometry, Seminars, Pure Mathematics
- Cost: Free
Michael Singer, University College London. Part of the geometry seminar series.
The Sen conjecture, made in 1994, makes precise predictions about the existence of L^2 harmonic forms on the monopole moduli spaces. For each positive integer k, the moduli space M_k of monopoles of charge k is a non-compact smooth manifold of dimension 4k, carrying a natural hyperkaehler metric. Thus studying Sen’s conjectures requires a good understanding of the asymptotic structure of M_k and its metric. This is a challenging analytical problem, because of the non-compactness of M_k and because its asymptotic structure is at least as complicated as the partitions of k. For k=2, the metric was written down explicitly by Atiyah and Hitchin, and partial results are known in other cases. In this talk, I shall introduce the main characters in this story and describe recent work aimed at proving Sen’s conjecture.
Michael Singer, University College London