Homological Mirror Symmetry for Not-So-Simple Singularities - Yanki Lekili

Explore the intricacies of homological mirror symmetry for invertible polynomials in this advanced mathematics lecture. Delve into joint research with Ueda, examining explicit conjectures that elucidate the workings of homological mirror symmetry for Milnor fibers. Discover proven cases, including simple singularities in various dimensions, where categories are equivalent to the derived category of Calabi-Yau completions of Dynkin quiver path algebras. Investigate the necessity of global deformations and their parametrization by moduli spaces of A∞ structures, identified with specific moduli spaces of polarized Calabi-Yau varieties. Focus on the Milnor fiber of x4 + y4 + z4 and its higher-dimensional generalizations as a rigorous example of homological mirror symmetry for not-so-simple singularities.