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Explore advanced mathematical concepts in algebraic geometry and mirror symmetry through this mathematical seminar lecture. Delve into the Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti, which establishes connections between Gromov-Witten invariants that count holomorphic curves in toric Calabi-Yau 3-manifolds and 3-orbifolds, and the Chekhov-Eynard-Orantin Topological Recursion invariants of their mirror curves. Discover the extended version of this conjecture with descendants, examining the correspondence between all-genus equivariant descendant Gromov-Witten invariants and oscillatory integrals (Laplace transforms) of Topological Recursion invariants along relative 1-cycles on equivariant mirror curves. Learn about the genus-zero correspondence as a manifestation of equivariant Hodge-theoretic mirror symmetry with integral structures. Investigate the proof of Hosono's conjecture in the non-equivariant setting, which demonstrates the equality between quantum cohomology central charges of compactly supported coherent sheaves and period integrals of holomorphic 3-forms along integral 3-cycles on Hori-Vafa mirrors. Gain insights into collaborative research findings developed with Bohan Fang, Song Yu, and Zhengyu Zong, presented by Chiu-Chu Melissa Liu from Columbia University as part of the M-Seminar series at Kansas State University.
