Title: Homological mirror symmetry for punctured Riemann surfaces from pair-of-pants decompositions
Speaker: Heather Lee
Speaker Info: Purdue and IAS
We will demonstrate one direction of HMS for punctured Riemann surfaces -- the wrapped Fukaya category of a punctured Riemann surface is equivalent to the matrix factorization category MF(X,W) of the toric Landau-Ginzburg mirror (X, W).Date: Thursday, November 3, 2016
The category MF(X,W) can be constructed from a Cech cover of (X,W) by local affine pieces that are mirrors of pairs of pants. We supply a suitable model for the wrapped Fukaya category for a punctured Rimemann surface so that it can also be explicitly computed in a sheaf-theoretic way, from the wrapped Fukaya categories of various pairs of pants in a decomposition. The pieces are glued together in the sense that the restrictions of the wrapped Floer complexes from two adjacent pairs of pants to their adjoining cylindrical piece agree.