Hyperkahler Mirror Symmetry
[HYBRID WORKSHOP] New FourDimensional Gauge Theories October 24, 2022  October 28, 2022
Location: SLMath: Eisenbud Auditorium, Online/Virtual
The broad contours of mirror symmetry for CalabiYau manifolds are wellunderstood by now: classical complexgeometric information is exchanged for a symplecticgeometric expansion defined in terms of a mirror manifold. In the hyperkahler context, one may expect to make still stronger statements. In this talk, I will explain how to do so in the case of the K3 manifold (and some degenerations thereof). Namely, the exact Ricciflat metric will have two expansions: (i) in terms of gauge theory on a fourtorus, and (ii) as corrected by a list of enumerative invariants. In particular, these two constructions are the topics of the talks by M. Zimet and L. Fredrickson earlier in the workshop; I will review these constructions before explaining how they are related by this strong form of mirror symmetry. This talk surveys a series of joint works with L. Fredrickson, S. Kachru, A. Vasy, and M. Zimet.
Hyperkahler Mirror Symmetry

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