There is a close relation between some aspects of algebraic geometry (in particular, birational geometry) and symplectic geometry via Gromov-Witten theory. For example, Kollar made some conjectures about the symplectic topology of rationally connected varieties, and Ruan speculated the existence of the so-called symplectic birational geometry. A theorem of Graber-Harris-Starr states that sections of rationally connected fibrations over a curve always exist, which has many important consequences in the theory of uniruled and rationally connected varieties. In this talk I will discuss the symplectic analogues of their result and how these results might be used to understand the conjectures of Kollar and Ruan.