Title: Diophantine equations, L-functions, and Selmer groups
Abstract: Diophantine equations have very long history in the study of mathematics. In modern number theory, various tools from algebraic geometry, complex analysis, representation theory are used to study these equations. In particular, the use of moduli spaces like Shimura varieties is crucial in the story. In this talk, I will explain how these methods are involved via examples of elliptic curves and some of their generalization.