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).
- Add multiplicities to the top-dimensional cones of \mathrm{DR}_g^{\mathrm{trop}}(A) to make it a tropical cycle.
- Compare the resulting cycle with the JPPZ formula. Start in genus g=1, where one has to compare codimension-1 classes.
- Further develop tropical intersection theory to make it work in higher genus.
Cite this as: AimPL: Double ramification cycles and integrable systems, available at http://aimpl.org/doubleramific.