|Oct 25, 2018
In this lecture series, I will give an introduction to SYZ mirror symmetry. I will start by reviewing Floer theory and its Morse theoretic approach. Then I will discuss the SYZ construction in details. By coupling with the Witten-Morse theory, I will show that how SYZ approach can be used to understand homological mirror symmetry in the semi-flat case (no singular fibers). The non-semi-flat case will be discussed mainly in dimension 2. We will see the effect of holomorphic disks contribution from the smooth Lagrangian fibers, whose locus on B form a set of geometric objects called walls. I will then discuss the wall crossing and scattering phenomena in the reconstruction problem. If time are allowed, I will discuss some recent progress on theta functions and geometric quantization in various situations.