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Explore joint research on the Zilber-Pink conjecture for Y(1)³ in this 33-minute mathematical conference talk. Learn about extensions to the G-function method that address curves intersecting boundary modular curves and discover unconditional results for points with few places of supersingular reduction. Examine how this work builds upon the 2012 Habegger-Pila results for asymmetric curves and recent advances including curves intersecting (∞, ∞, ∞) and curves intersecting special boundary points. Understand the mathematical techniques used to prove these new cases and their significance in Diophantine geometry. The presentation covers collaborative research with M. Orr from Manchester and G. Papas from the Institute for Advanced Study, demonstrating how the G-function method can be extended beyond previously known cases to handle more complex geometric configurations in the context of the Zilber-Pink conjecture.
