3620 South Vermont Avenue, Los Angeles, CA 90089

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Xin Jin, Boston College

Abstract: I’ll present recent work on mirror symmetry for the affine Toda systems, which can be viewed as a Betti Geometric Langlands correspondence (after Ben-Zvi—Nadler) in the wild setting. More explicitly, we realize the affine Toda system (associated to a complex semisimple group) as a moduli space of Higgs bundles on P^1 with certain automorphic data, and the dual side is the group version of the universal centralizer (associated to the dual group), which is a wild character variety. We show that the wrapped Fukaya category of the former is equivalent to the category of coherent sheaves of the latter. The proof uses my previous result on the mirror symmetry for the (usual) Toda systems, also known as the universal centralizers. This is joint work with Zhiwei Yun.

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