Proves homological mirror symmetry linking the wrapped Fukaya category of the affine Toda system for G to coherent sheaves on the regular centralizer for G^vee, as a geometric Langlands equivalence for P1 with mildest wild ramification at 0 and infinity.
Trinh.Algebraic Braids and Geometric Representation Theory
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Mirror Symmetry of the Affine Toda Systems
Proves homological mirror symmetry linking the wrapped Fukaya category of the affine Toda system for G to coherent sheaves on the regular centralizer for G^vee, as a geometric Langlands equivalence for P1 with mildest wild ramification at 0 and infinity.