Deformations and Mutations of Affine Gorenstein Toric Varieties

Explore the mathematical relationship between one-parameter deformations of affine Gorenstein toric varieties and mutations of Laurent polynomials in this 54-minute conference talk. Learn how deformations of a toric variety X, determined by a polytope P, correspond to mutations of a Laurent polynomial f with Newton polytope P. Discover the construction methods for components of deformation spaces in three-dimensional cases through mutation techniques. Gain insights into advanced algebraic geometry concepts including toric varieties, polytopes, and singularity theory applications. The presentation was delivered at the "New Developments in Singularity Theory" conference, a joint IMSA & ICMS event supported by the Simons Foundation, National Science Foundation, and the University of Miami.