# Number Theory Seminar

*,*Department of Mathematics, Statistics, & Computer Science

*,*University of Illinois, Chicago

*,*

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 the Ax-Lindemann-Weierstrass (ALW) Theorem and its role in his proof of the AndrĂ©-Oort conjecture.

In this talk we will discuss how an entirely new approach, using the model theory of differential fields as well as other differential tools, can be used to prove functional transcendence results (including ALW) for Fuchsian automorphic functions and other covering maps. We will also explain how cases of the AndrĂ©-Pink conjecture can be obtained using this new approach. This is joint work with D. Blazquez-Sanz, G. Casale and J. Freitag.