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Explore a comprehensive lecture on the P=W conjecture delivered by Tony Pantev from the University of Pennsylvania. Delve into the character varieties and their known results, generalizations, and applications. Examine the mirror version of the P=W conjecture in the context of Fano mirror symmetry and its connection to the Hodge theory of Landau-Ginzburg models. Investigate refinements of the mirror P=W problem within SYZ mirror symmetry. Learn about recent work by Sukjoo Lee on applying gluing in relative mirror symmetry to the mirror P=W conjecture and the Hodge and deformation theory of hybrid Landau-Ginzburg models. Gain insights from this talk, which is based on ongoing joint work with Harder and Katzarkov.
