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Title:
Non-abelian Hodge theory in dimension one, Floer homology and periodic monopoles
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Abstract:
I am going to expian a conjectural generalization of the non-abelian Hodge theory of Simpson which in dimension one includes not only bundles with connections but also q-difference and elliptic difference equations. The approprite framework is the one of generalized Riemann-Hilbert correspondence for complex symplectic manifolds proposed by Kontsevich and myself, which uses Fukaya categories.
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