Eisenstein series are an essential ingredient in the theory of automorphic
forms with numerous applications to number theory and arithmetic geometry.
In this talk, we investigate Eisenstein series associated to special
points on finite volume hyperbolic Riemann surfaces. As it turns out, these Eisenstein
series do not sit in isolation, but, rather, various relations exist. This
motivates to study analogues of the Takhtajan-Zograf form on the moduli space of
Riemann surfaces with n marked weighted points using so-called elliptic
Eisenstein series.