Just as we study varieties by utilizing vector bundles over them, we
often study symplectic manifolds by utilizing holomorphic curves.
While holomorphic curves are by far the most useful tool in
symplectic geometry, the analytical details can often be a
bottleneck. In this talk, we'll talk about how the most computable
cases of holomorphic curve theory may conjecturally be recovered by
purely topological (i.e., non-analytical) means---namely, through the
algebraic structure inherent in cobordisms. As an example theorem, we
will show that if two exact closed Lagrangians submanifolds are
related by an exact Lagrangian cobordism, then their Floer theories
are identical in a very strong sense.