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Explore the intricacies of counting rational points on modular curves of genus 0 over number fields in this comprehensive lecture by Peter Bruin. Delve into advanced topics in arithmetic geometry as part of the "Rational Points on Modular Curves" program organized by the International Centre for Theoretical Sciences. Learn about the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields K and subgroups H of GL2(Z/NZ). Gain insights into the geometry of modular curves, Q-rational points, classical and non-abelian Chabauty methods, and related computational techniques. Benefit from this expert presentation that bridges advanced topics with practical examples, suitable for researchers and students interested in elliptic curves, modular forms, and modular curves in the field of arithmetic geometry.
