Abstract: We introduce the notion of heights in Diophantine geometry by first considering the canonical height pairing on an elliptic curve. We discuss the role it plays in the Birch and Swinnerton-Dyer (BSD) conjecture and use this to motivate a discussion of p-adic heights and the p-adic BSD conjecture. We will then describe recent joint work with Amnon Besser on computing p-adic heights on Jacobians of hyperelliptic curves.

This talk will be accessible to graduate students.