The cone conjecture in relative dimension 2

Pretalk title: Cones of divisors, the cone theorem, and the cone conjecture.

Pretalk abstract: The finite-dimensional vector space of divisors modulo numerical equivalence on a projective variety X contains several convex cones that tell you very concrete and useful geometric information about X. We will explore the structure of a few of these cones through theorems and examples, building up to some current work of myself and Joaquín Moraga.

Talk title: The cone conjecture in relative dimension 2

Abstract: We motivate the cone conjecture, discussing its uses and progress that has been made, and then discuss some work of myself and Joaquín Moraga. We will outline the proof of the relative cone conjecture in relative dimension 2.