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Explore how machine learning models can predict Euler factors of elliptic curves in this 55-minute conference talk from Harvard CMSA's Math and Machine Learning Reunion Workshop. Discover the mathematical challenge of determining traces of Frobenius for elliptic curves, where traditional algorithms struggle to efficiently compute remaining $a_p(E)$ values even when enough data exists to uniquely identify an isogeny class. Learn about preliminary research demonstrating that ML models can predict the next trace of Frobenius with surprising accuracy using relatively few nearby entries, and examine potential explanations for this unexpected performance. Gain insights into the intersection of algebraic geometry and machine learning through collaborative research involving multiple institutions, as the speaker presents findings on using computational methods to solve classical problems in number theory related to elliptic curves and their arithmetic properties.
