2012/12/18 by Mark Gross, Gross, Mark · 4 citations
Mathematics · #14J32 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG #msc:14J32
paper · pdf · doi:10.48550/arxiv.1212.4220
For Current Developments in Mathematics, 2012, 67 pages
arxiv created 2013/09/20 · arxiv updated 2013/09/23
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and thinking about the SYZ conjecture since its introduction in 1996. We begin with the original differential geometric conjecture and its refinements, and explain how it led to the algebro-geometric program developed by myself and Siebert. After explaining the overall philosophy, I explain how recent results fit into this program.