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Explore advanced mathematical research on the Zilber-Pink conjecture for Y(1)³ in this hour-long conference talk from the Workshop on Special Cycles and Related Topics at the Institute for Advanced Study. Delve into work in progress with M. Orr from Manchester and G. Papas from Weizmann Institute that extends beyond the known results for asymmetric curves established by Habegger-Pila in 2012. Learn about the G-function method and its recent applications to various cases, including curves intersecting (∞,∞,∞) and curves intersecting special points in the boundary. Discover how this research extends the method to handle curves intersecting boundary modular curves and provides unconditional results for points with few places of supersingular reduction. Gain insights into cutting-edge developments in arithmetic geometry and the ongoing efforts to prove the Zilber-Pink conjecture in this specific context.
