Abstract: "In 1974 Arakelov introduced an intersection theory for metrized line bundles on smooth projective curves over number fields. Ten years later, Faltings extended this theory widely. For example, he proved an analogue of the classical Noether formula. This formula additionally includes an invariant of compact Riemann surfaces, now called Faltings' delta invariant. In this talk, we will give new formulas of Faltings' delta invariant in terms of integrals of theta functions. This has several applications: We obtain a lower bound for delta only in terms of the genus and we give a canonical extension of delta to the moduli space of abelian varieties. As applications to Arakelov theory, we can for example bound the heights of Weierstraß points in terms of the Faltings height."