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Explore a detailed mathematics lecture examining the SYZ approach to mirror symmetry for log Calabi-Yau pairs, with particular focus on cases where D contains exceptional rational curves. Delve into recent findings on Hirzebruch surfaces through Honghao Jing's ongoing research, and investigate a four-dimensional example showcasing how stable discs with negative Maslov index affect wall-crossing corrections in mirror geometry. Learn about a Morse-theoretic methodology for constructing corrected mirrors using the geometry of treed holomorphic discs, drawing from Keeley Hoek's PhD thesis work. Gain advanced insights into the geometric complexities of non-Fano log Calabi-Yau pairs and their mirror symmetry properties through Harvard University professor Denis Auroux's comprehensive analysis.
