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Learn about matrix factorizations and their relationship to Fukaya categories of surfaces in this mathematics lecture that explores the classification of indecomposable objects in maximal Cohen-Macaulay modules over non-isolated surface singularity. Delve into homological mirror symmetry and its connection to the Fukaya category of pair-of-pants surface, examining how immersed curves equipped with local systems correspond to indecomposable MCM modules. Discover the explicit canonical form of matrix factorizations of xyz and their geometric applications through the work of Burban-Drozd, Abouzaid-Auroux-Efimov-Katzarkov-Orlov, and Cho-Hong-Lau's localized mirror functor, culminating in insights from recent collaborative research by Cho-Jeong-Kim-Rho and Cho-Rho.
