## Algebraic Geometry Seminar

Eric Riedl

Notre Dame

Hyperbolicity of hypersurfaces in projective space

**Abstract:**We discuss several related notions of hyperbolicity in projective space, focusing particularly on algebraic hyperbolicity and Brody hyperbolicity. We discuss what is known about these notions for very general hypersurfaces in projective space. In joint work with Coskun, we prove that quintic hypersurfaces in P^3 are algebraically hyperbolic, finally settling the last case of a conjecture of Demailly. In joint work with David Yang, we show that (a slightly stronger version of) the Green-Griffiths-Lang Conjecture implies the Kobayashi Conjecture.

Wednesday March 20, 2019 at 4:00 PM in 427 SEO