Title: Microlocal sheaf theory and Lagrangian handlebodies

Abstract: You can learn some things about symplectic manifolds M and their Lagrangian submanifolds L by studying Kashiwara and Schapira (that's the "microlocal sheaf theory" in the title). The cheapest available results along these lines apply to cotangent bundles, like M = R^{2n}, but they are not always boring if L is not boring. I will discuss the Harvey-Lawson Lagrangians in R^6, and some analogs (the Lagrangian handlebodies in the title), from this point of view. One can make a sheaf-theoretic computation here that should match the open Gromov-Witten invariants of (M,L) in different framings, though those OGW invariants do not yet have a mathematical definition. The talk is based on joint work with Linhui Shen and Eric Zaslow.