The three of us will give a sketch of what Kontsevich's homological mirror symmetry conjecture predicts, then demonstrate homological mirror symmetry in a simple example: CP^1, whose mirror is a Landau-Ginzburg model.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/5518