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Seminar by Joseph Chan (University of Melbourne, Australia)

Title: (N-1)-interval discrete Nahm equations for SU(N) monopoles in hyperbolic space

2015.08.06 | Jane Jamshidi

Date Mon 10 Aug
Time 16:30 17:30
Location Aud. D3 (1531-215)


Braam and Austin in 1990, proved that SU(2) magnetic monopoles in hyperbolic space H^3 are the same as solutions of the discrete Nahm equations. I apply equivariant K-theory to the ADHM construction of instantons/holomorphic bundles to get the (N-1)-interval discrete Nahm equations for the SU(N) case. During its evolution, the matrices of the (N-1)-interval discrete Nahm equations jump in dimensions and (at least to the author's knowledge) this behaviour has not been observed in discretisations of evolution equations before. A secondary result is that the monopole field at the boundary of H^3 determines the monopole.