2018/11/22 by Ziming Nikolas, Ma, Ziming Nikolas
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1811.09042
openalex publication_date 2018/11/22 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28
This is a survey article on the recent progress in understanding the Strominger-Yau-Zaslow (SYZ) mirror symmetry conjecture, especially on the effect of quantum corrections, via Witten-Morse theory using the program first depicted by Fukaya to obtain an explicit relation between differential geometric operations, e.g. wedge product of differential forms and Lie-bracket of the Kodaira-Spencer complexes, with combinatorial structures, e.g. Morse A_∞ structures and scattering diagrams.