Smoothing Gorenstein Toric Singularities and Mirror Symmetry

Explore a one-hour lecture on the mathematical correspondence between one-parameter deformations of affine Gorenstein toric varieties and Laurent polynomial mutations, focusing on two-dimensional Newton polytopes and their smoothing properties. Delve into the proof that demonstrates how Gorenstein toric varieties admit smoothing when their associated Newton polytope can mutate to a smooth polygon under specific conditions. Learn about the practical applications of these concepts in mirror symmetry and deformation theory, particularly for polygons that are affine equivalent to facets of reflexive three-dimensional polytopes, and understand how these principles extend to Fano toric varieties.