Jeff Hicks, University of California, Berkeley

Title: Wall Crossing and Lagrangian Cobordisms.

Abstract: It is an expectation that the count of holomorphic disks with boundary on a Lagrangian submanifold L assembles into a holomorphic function W on the moduli space of Lagrangian submanifolds. In practice, this statement is only locally true -- as one calculates W  over a family of Lagrangians it is possible that W develops a discontinuity when disks bubble. One can correct for these discrepancies by appropriately weighting the count of holomorphic disks. These weights modify the complex structure on the moduli space of Lagrangian submanifolds via so-called "wall-crossing transformations.'' In this talk, we show that one can calculate these wall-crossing transformations via counts of holomorphic disks on Lagrangian cobordisms instead.