Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4

Delve into the fourth lecture of a comprehensive series on modular forms, elliptic curves, and modular curves presented by Eknath Ghate at the International Centre for Theoretical Sciences. Explore advanced concepts in arithmetic geometry as part of a two-week program focused on rational points on modular curves. Gain insights into the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. Discover the connections between elliptic curves, modular forms, and modular curves as central objects in arithmetic geometry. Engage with topics such as the geometry of modular curves, Q-rational points, classical and non-abelian Chabauty methods, and related computational aspects. Benefit from a balanced approach that combines advanced topics with practical examples, making it suitable for both experienced researchers and young mathematicians entering the field.