|Jun 27, 2022
In this talk, we introduce the ongoing programme of Gross-Siebert and Gross-Hacking-Keel to expand the ideas of SYZ mirror symmetry to a broader class of symplectic manifolds. We first recall the SYZ mirror symmetry construction, and its limitations. To analyze how the mirror should behave near critical torus fibers, we introduce the language of tropical geometry and explain SYZ mirror symmetry for Calabi-Yau manifolds in this context. We end by giving some recent developments in this direction. The talk will be mostly based on two expository papers of Mark Gross - "Theta Functions and Mirror Symmetry", and "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations".