The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1

Explore the Chabauty-Coleman-Kim Method in this comprehensive lecture, the first in a series on rational points on modular curves. Delve into advanced arithmetic geometry concepts as part of the "Rational Points on Modular Curves" program organized by the International Centre for Theoretical Sciences. Learn about the theoretical foundations and practical applications of this method, which is crucial for studying rational points on varieties. Gain insights into elliptic curves, modular forms, and modular curves as central objects in arithmetic geometry. Discover how modular curves serve as moduli spaces for elliptic curves with extra level structures. Understand the program's objective of determining K-rational points on modular curves XH(K) for various fields and subgroups. Benefit from an advanced introduction to the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Engage with a balanced approach that combines advanced topics with practical examples, making it suitable for researchers at various levels. Join a diverse group of international experts in arithmetic geometry to explore current research and foster future collaborations in this field.