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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Mirror symmetry for Fano surfaces via scattering and tropical curves

## Mirror symmetry for Fano surfaces via scattering and tropical curvesAdd to your list(s) Download to your calendar using vCal - Tim Gräfnitz, University of Cambridge
- Wednesday 11 May 2022, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Dhruv Ranganathan. Mirror symmetry relates Fano varieties to Landau-Ginzburg models – non-compact varieties together with a potential function W. Gross-Siebert developed an algorithmic construction of mirrors via algebro-combinatorial objects called scattering diagrams and broken lines. I describe the combinatorial aspects of this construction for the easiest case of a Fano surface – P2 relative to an elliptic curve E. Mirror symmetry predicts a relation between curve counts for (P2,E) and complex structure deformations of its mirror. On the combinatorial level this translates to a correspondence between curve counts for (P2,E) and scattering diagrams resp. broken lines. Such a correspondence can be proved using tropical geometry. If time permits, I will also talk about joint work with Helge Ruddat and Eric Zaslow in which we relate the Landau-Ginzburg potential defined via broken lines to the open mirror map of Aganagic-Vafa branes in framing zero. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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