2018/11/22 by Ziming Nikolas, Ziming Nikolas Ma, Ma, Ziming Nikolas
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Bracket #Computer science #Conjecture #Differential (mechanical device) #Differential Geometry (math.DG) #Differential calculus #Engineering #FOS: Mathematics #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mirror symmetry #Morse code #Morse theory #Physics #Pure mathematics #Symmetry (geometry) #Symplectic Geometry (math.SG) #Wedge (geometry) #math.AG #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.1811.09042
published in arXiv (Cornell University) (Cornell University) · Conference (Gromov-Witten theory, Gauge Theory and Dualities) survey article with 36 pages, to be appeared in CMA proceedings
arxiv created 2018/11/22 · openalex publication_date 2018/11/22 · arxiv updated 2018/11/26 · 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.