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I study the geometry, deformations, and quantisations of moduli spaces of connections on (generalisations of) Riemann surfaces, mainly using techniques from complex Poisson/symplectic geometry, representation/Lie theory, and the functional analysis of Hilbert spaces; but also in particular geometric/deformation quantisation.
This line of study lies at the interface of low dimensional topology/geometry, representation/Lie theory, and mathematical physics, and leads in particular to mathematical formalisations of classical/quantum field theories with gauge/conformal symmetries.
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