Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automorphic functions
Over the last decades, following works around the Pila-Wilkie counting theorem in the context of o-minimality, there has been a surge in interest around functional transcendence results, in part due to their connection with special points conjectures. A prime example is Pila's modular ALW Theorem and its role in his proof of the André-Oort conjecture.
In this talk we will discuss how an entirely new approach, using the model theory of differential fields, can be used to prove the Ax-Lindemann-Weierstrass (ALW) Theorem with derivatives for Fuchsian automorphic functions - a direct generalization of Pila’s ALW theorem. We will also explain how new cases of the André-Pink conjecture can be obtained using this new approach. This is joint work with G. Casale and J. Freitag.