Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2

Delve into the second lecture of an advanced series on modular forms, elliptic curves, and modular curves presented by Eknath Ghate at the International Centre for Theoretical Sciences. Explore key concepts in arithmetic geometry over the course of 1 hour and 40 minutes, building upon the foundations laid in the previous session. Gain insights into the intricate relationships between these mathematical objects, which are central to the study of rational points on varieties. Examine the theoretical framework and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. Enhance your understanding of the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Benefit from a balanced approach that combines advanced topics with practical examples, making this lecture suitable for researchers and graduate students in number theory and algebraic geometry.