Master Degree Project Presentation: Homological mirror symmetry for crepant resolutions of compound A_n singularities

Abstract: Homological mirror symmetry predicts a deep equivalence between symplectic geometry and algebraic geometry, relating Fukaya categories on one side to derived categories of coherent sheaves on the other. This thesis studies a case of homological mirror symmetry for crepant resolutions of compound A_n singularities, whose mirrors are described by certain Morse–Bott–Lefschetz fibrations. In this talk, I will introduce Fukaya categories, discuss their computation in this setting, and explain how this leads to the desired mirror equivalence.