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SUMMARY:Rodrigo Barbosa (Simons Center for Geometry and Physics)
DTSTART:20200729T183000Z
DTEND:20200729T200000Z
DTSTAMP:20260423T021728Z
UID:BRAG/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BRAG/18/">St
 ring Dualities\, Higgs Bundles and $G_2$ Geometry</a>\nby Rodrigo Barbosa 
 (Simons Center for Geometry and Physics) as part of Brazilian algebraic ge
 ometry seminar\n\n\nAbstract\nDualities in string/M theory often provide n
 ovel perspectives for deformation problems in geometry. In one such instan
 ce\, involving Large $N$ duality in the B-model\, one can construct a fami
 ly of ALE-fibered Calabi-Yau threefolds over a Riemann surface $S_g$ ($g \
 \geq 2$) whose Jacobian integrable system is isomorphic to the $G$-Hitchin
  system over $S_g$\, where $G$ is the compact real form associated to the 
 ALE type via the McKay correspondence. I will explain a different physical
  framework\, involving M-theory/Type IIA duality\, that gives an analogous
  construction of ALE-fibered $G_2$-manifolds parametrized by spectral cove
 rs of certain "smooth Higgs bundles" over a $3$-manifold. I will explain h
 ow this theory connects with Donaldson's theory of Kovalev-Lefschetz fibra
 tions and how it presents a window for applying algebro-geometric techniqu
 es to moduli problems in $G_2$-geometry. Time permitting\, I will comment 
 on a second algebro-geometric model for the moduli space of (complexified)
  $G_2$-structures derived from SYZ Mirror Symmetry for the Type IIA geomet
 ry.\n
LOCATION:https://researchseminars.org/talk/BRAG/18/
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