| I will discuss a correspondence between the number of algebraic and tropical elliptic curves on toric surfaces with fixed j-invariant. The proof combines ideas from tropical geometry with recent tools from log geometry. As an application, we obtain a new enumerative formula for Hirzerbruch surfaces, relating the number of such curves with the number of rational curves having mild tangency with the boundary. In addition, I will show how the correspondence theorem is used to recover Pandharipande's formula for the projective plane. This is joint work with Dhruv Ranganathan. |