BIRS Workshop Lecture Videos
Homological mirror symmetry for birational cobordisms with trivial center Kerr, Gabriel
It has been known since Bondal and Orlov's work on semi-orthogonal decompositions that for blow-ups, projective bundles and certain flips f : X ---> Y, one may decompose the derived category of D(X) = < D(Y), C >. In this talk I will describe the mirror LG model to C when f is a birational cobordism with trivial center. Diemer-Katzarkov-K. conjectured that this was a Fukaya-Seidel category FS (W) of a potential W from a higher dimensional pair of pants to the punctured plane. I will explain a recent proof of this conjecture. The classical version of HMS for weighted projective spaces of arbitrary dimension then will be observed as a corollary.
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