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Explore the latest developments in singular moduli for real quadratic fields in this comprehensive lecture by Jan Vonk at the International Centre for Theoretical Sciences. Delve into advanced topics in arithmetic geometry, focusing on rational points on modular curves. Learn about the geometry of modular curves, Q-rational points, classical and non-abelian Chabauty methods, and related computational aspects. Gain insights into the study of K-rational points on modular curves XH(K) for various fields K and subgroups H of GL2(Z/NZ). Discover the connections between elliptic curves, modular forms, and modular curves as central objects in arithmetic geometry. Benefit from a balanced approach that combines advanced topics with practical examples, making it suitable for both experienced researchers and young mathematicians in the field.
