Roger Bielawski: Quasimonopoles and the asymptotics of monopole metrics
I shall introduce and discuss moduli spaces of quasimonopoles — hyperkähler manifolds which approximate the SU(2)-monopole metric with exponential accuracy in appropriate asymptotic regions, and possess a torus symmetry required in the Segal–Selby approach to the Sen conjecture. This is joint work with Sergey Cherkis and Jacques Hurtubise.
Cliff Taubes: Analysis for the Vafa–Witten equations
I plan to explain and illustrate some of the salient analysis issues with regards to potential use of Vafa–Witten equation solutions to define smooth invariants for 4-dimensional manifolds. As it turns out, most of iconic gauge theory plays a role in the story: Bogolmony monopoles on ℝ3, anti-self dual instantons on ℝ4, flat SL(2; ℂ) connections on Riemann surfaces, and then some novelties (ℤ/2 harmonic differential forms).