SYZ mirror symmetry from Witten-Morse theory

Abstract

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 $A_{\infty }$ structures and scattering diagrams.

Conference (Gromov-Witten theory, Gauge Theory and Dualities) survey article with 36 pages, to be appeared in CMA proceedings