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Labeled floor diagrams for plane curves

Sergey Fomin, Grigory Mikhalkin (2010)

Journal of the European Mathematical Society

Floor diagrams are a class of weighted oriented graphs introduced by E. Brugallé and the second author. Tropical geometry arguments lead to combinatorial descriptions of (ordinary and relative) Gromov–Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In a number of cases, these descriptions can be used to obtain explicit (direct or recursive) formulas for the corresponding enumerative invariants. In particular, we use this approach to enumerate rational...

Landau-Ginzburg models in real mirror symmetry

Johannes Walcher (2011)

Annales de l’institut Fourier

In recent years, mirror symmetry for open strings has exhibited some new connections between symplectic and enumerative geometry (A-model) and complex algebraic geometry (B-model) that in a sense lie between classical and homological mirror symmetry. I review the rôle played in this story by matrix factorizations and the Calabi-Yau/Landau-Ginzburg correspondence.

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