Geometry and Physics Seminar: Colin Diemer

One version of homological mirror symmetry relates the algebraic geometry of certain varieties to the symplectic topology of a Lefschetz pencil. Extracting symplectic (i.e. Floer theoretic) invariants from these fibrations is quite difficult, even in simple examples. I'll review some recent proposals (particularly from Kapranov-Kontsevich-Soibelman and Diemer-Kerr-Katzarkov) for deforming symplectic fibrations into more tractable components. The corresponding mirror theory appears to be closely related to birational geometry and the Mori program.