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Title:
Algebraic geometry of Gaiotto correspondence and quantization of Higgs bundles
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Abstract:
In this talk, I will start with reporting the newly established solution to a conjecture of Gaiotto, due to Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, Raffe Mazzeo, Andrew Neitzke, and myself. The conjecture states that a particular scaling limit of the non-Abelian Hodge correspondence gives a biholomorphic mapping from the Hitchin section of the moduli of G-Higgs bundles to the moduli of Lie(G)-opers in the Betti-moduli space. Here, G is a complex simple Lie group. The process can be understood as a quantization, where C-star action on the Higgs bundle side corresponds to the h-bar deformation family of opers. Then we describe the extension of the biholomorphic correspondence to open neighborhood of the holomorphic Lagrangians on each side. This gives a correspondence totally different from non-Abelian Hodge correspondence. This part of the story is based on a joint work with Dumitrescu, Priya Kshirsagar, and Ruifang Song.
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