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Michael Thaddeus : Mirror Symmetry and Langlands Duality

Strominger, Yau and Zaslow have proposed that Calabi-Yau mirror partners should be families of special Lagrangian tori over the same base which are dual to each other. I will exhibit some striking evidence for this proposal: pairs of Calabi-Yau orbifolds satisfying the requirements of SYZ for which the expected equality of stringy Hodge numbers can be completely verified. This is in a sense the first enumerative evidence supporting SYZ. The construction I will present is the first of several suggesting a general principle: for any construction using a compact Lie group to construct a Calabi-Yau, mirror partners arise from applying the construction to Langlands dual groups.

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