Rational Points on Modular Curves - Lecture 2

Delve into the second lecture of a comprehensive series on Rational Points on Modular Curves, delivered by Jan Vonk at the International Centre for Theoretical Sciences. Explore advanced concepts in arithmetic geometry, focusing on the study of rational points on modular curves. Gain insights into the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Discover 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). Engage with a balanced presentation of advanced topics and practical examples, designed to deepen understanding of elliptic curves, modular forms, and modular curves as central objects in arithmetic geometry. Benefit from this 1 hour and 35 minute lecture, part of a program bringing together experts in arithmetic geometry to share ideas and current research, encouraging participation from young researchers and underrepresented groups in the field.