Solving equations involving the j-function and its derivatives

The j-function is a central player in the study of elliptic curves. It satisfies many interesting algebraic properties, but there many things still unknown. In this talk we will discuss the problem of trying to solve polynomial equations that involve the j-function and its first two derivatives, and we will discuss some important cases that can be solved. This is joint work with Vahagn Aslanyan and Vincenzo Mantova.