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Rodrigo Barbosa: Lectures

April 10, 2019
TITLE: Deformations of G2-structures, String Dualities and Flat Higgs Bundles

ABSTRACT: We study M-theory compactifications on (resolutions of) G2-orbifolds given by total spaces of ALE-fibrations over a compact flat Riemannian 3-manifold Q. The flatness condition allows an explicit description of the moduli space of supersymmetric vacua: it is parametrized by flat sections of a bundle of Brieskorn-Grothendieck resolutions over Q. Moreover, when instanton corrections are neglected, we have an explicit description of the moduli space for the IIA dual compactification in terms of flat Higgs bundles on Q. We explain how it suggests a new interpretation of SYZ mirror symmetry, while also providing a description of G2-structures in terms of IIB-branes. The net result is two algebro-geometric descriptions of the moduli space of complexified G2-structures: one as a character variety, and another as a Hilbert scheme of points on a threefold. We show the moduli spaces match in an important example. This is joint work with Tony Pantev.
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