On the Solutions of Certain Diophantine Equations Over Totally Real Fields

Explore a 30-minute lecture on solving specific Diophantine equations over totally real fields, presented by Satyabrat Sahoo at the International Centre for Theoretical Sciences. Delve into advanced topics in arithmetic geometry as part of the "Rational Points on Modular Curves" program. Gain insights into the study of rational points on varieties, with a focus on modular curves. Learn about elliptic curves, modular forms, and their significance in arithmetic geometry. Discover techniques for determining K-rational points on modular curves XH(K) for various fields and subgroups. Engage with both theoretical and computational aspects of this fascinating area of mathematics, suitable for researchers and advanced students in number theory and related fields.