Bernd Siebert, University of Texas Austin: From toric degenerations to intrinsic mirror symmetry II

Bernd Siebert, University of Texas at Austin: From toric degenerations to intrinsic mirror symmetry II
I will survey my joint program with Mark Gross providing an algebraic-geometric perspective on the SYZ dual torus fibrations in mirror symmetry: Our original synthetic approach constructed mirror dual degenerating families with central fibers unions of toric varieties via wall structures. More recently, we were able to define wall structures to construct the mirror toric degenerations via Gromov-Witten theory in general Calabi-Yau geometries ("intrinsic mirror symmetry"). Taken together this provides an algebraic-geometric implementation of the quantum corrections to the complex structure of the mirror SYZ fibration compatibly with both the original differential-geometric and the non-archimedean frameworks.