Double ramification cycles and integrable systems

7. The Tropical DR cycle

Proposed by Andreas Gross:

There exist tropical DR loci $\mathrm{DR}_g^{\mathrm{trop}}(A)$ (Ulirsch, Zakharov) in the tropical moduli spaces $\mathcal M_{g,n}^{\mathrm{trop}}$ of curves. They are the tropicalizations of the cycles $\mathrm{DR}^{\mathrm{adm}}_g(A)$.

1. Add multiplicities to the top-dimensional cones of $\mathrm{DR}_g^{\mathrm{trop}}(A)$ to make it a tropical cycle.
2. Compare the resulting cycle with the JPPZ formula. Start in genus $g=1$, where one has to compare codimension-$1$ classes.
3. Further develop tropical intersection theory to make it work in higher genus.