Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automorphic functionsÌý
Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automorphic functionsÌý
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Passcode:ÌýThe three digit integer that is the cube of the sum of its digits
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Over the last decades,Ìýfollowing 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.Ìý
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 alsoÌýexplain 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.
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