#### Rational Surfaces in Smooth Hypersurfaces

**Roya Beheshti** (Queens University, Ontario)

**Abstract:** It is conjectured that a general hypersurface of degree n in P^n is not unirational for n > 3. I'll talk about some questions, arising from this conjecture, on rational surfaces contained in a smooth hypersurface of degree n in P^n. I'll also talk about the birational geometry of the space of rational curves of low degree contained in such a hypersurface. This is joint work with Jason Starr.