A tropical approach to enumerative geometry

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Supertropical algebra (2008, background): “As developed in [1, 2, 3, 4, 6, 7, 21, 24, 27, 28, 29, 30], the max-plus algebra (or dually, the min-plus algebra) lies at the foundation of “tropical algebra” and “tropical geometry.”
Logarithmic equivalence of Welschinger and Gromov-Witten invariants (2004, background): “Shustin [6, 7], we studied the toric unnodal Del Pezzo surfaces with tautological real structure and showed that for these surfaces Welschinger and Gromov-Witten invariants are equivalent in the logarithmic scale, if all or almost all fixed points in the generic collection are real.”
Tropical geometry and correspondence theorems via toric stacks (2010, methodology): “An algebra-geometric proof of Mikhalkin’s theorem based onViro’s patchworking method was proposed by Shustin [13] in 2005.”
A Caporaso-Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces (2006, background): “Notice that Theorem 1 can also be proved via the study of non-parameterized plane tropical curves in the spirit of [8].”