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Explore the intricate relationship between mutations and deformations of Gorenstein toric varieties through the lens of logarithmic geometry in this conference talk. Learn how deformations of Gorenstein toric varieties connect to the concept of mutations, drawing inspiration from mirror symmetry theory. Discover the relevant mathematical notions, examine current conjectures and established results in the field, then delve into a novel approach utilizing logarithmic geometry. Review preliminary findings that demonstrate the viability of this new methodology, representing collaborative research with Alessio Corti and Helge Ruddat. Gain insights into advanced algebraic geometry concepts including toric varieties, Gorenstein conditions, mutation theory, and logarithmic resolutions, while understanding their applications in modern singularity theory and mirror symmetry.
