Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1

Dive into the first 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 the fundamental concepts of arithmetic geometry in this 1 hour and 32 minute session, part of the "Rational Points on Modular Curves" program. Gain insights into the intricate relationships between these central objects of arithmetic geometry, setting the foundation for understanding their role in the study of rational points on varieties. Discover how modular curves serve as moduli spaces for elliptic curves with additional level structures, and prepare for an advanced journey into both theoretical and computational aspects of determining K-rational points on modular curves for various fields and subgroups.