4th October: Yuan Yang

Title: Decompose the canonical height.

Abstract: height functions are a kind of very useful but mysterious functions in number theory. We can talk about the height of a rational number, the height of an algebraic number, and the canonical height of a rational point on en elliptic curve. In this talk, I will mainly focus on the canonical height function of a rational point on en elliptic curve: it is used in proving the Mordell-Weil theorem, and it is such a mysterious function, with secrets that no one knows why. I will gently introduce how to decompose it into local pieces, and discuss how it is a variant of the arithmetic intersection theory.