B. Siebert: “A Tropical View on Landau-Ginzburg Models”

Here are my notes from Siebert’s talk at the Extremal Laurent Polynomials workshop at Imperial:



  • An overview of toric degenerations and the Gross–Siebert picture
  • Examples: a pencil of quartics in \PP^3 and a pencil of elliptic curves in \PP^2
  • the Gross–Siebert Reconstruction Theorem
  • Mirror Symmetry and the discrete Legendre Transform
  • Landau–Ginzburg models; the Hori–Vafa mirror
  • how to extend the superpotential from the central fiber to the whole of the mirror family in such a way that the resulting superpotential is proper
  • Example: \PP^2, flattening the boundary of the polyhedral complex
  • Broken lines and scattering

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