In this series of 4 lectures, I will survey some recent work on Faltings heights of CM abelian varieties and applications.
In the first lecture, I will talk about some general conjectures about Faltings heights including ABC conjecture, André-Oort conjecture, and Landau-Siegel zero conjecture, etc.
In the second lecture, I will talk about some decompositions of Faltings heights of CM abelian varieties into sums of small pieces and their relations with heights of CM points on Shimura curves.
In the third lecture, I will talk about Xinyi Yuan’s recent work on Faltings of CM points on Shimura curves as an extension of Gross-Zagier formula.
In the last lecture, I will talk about Yun-Zhang’s recent work on Faltings heights of CM points on the moduli of Shtukas.
