Time: Dec. 10, 2019, 15:30-17:00; Dec. 12, 2019 14:30-16:00
The goal of these two talks is to present a functional transcendence result. We will prove the Ax-Schanuel theorem for abelian varieties over the complex field, which has numerous applications in number theory.
The first talk will focus on the o-minimal geometry. At the end we will explain the Pila-Wilkie counting theorem. The second talk will explain the Ax-Schanuel theorem for complex abelian varieties. We will start with the statement and give its proof by the o-minimal geometry.