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Using A1 enumerative geometry Larson and Vogt have provided an enriched count of the
28 bitangents to a quartic curve. In this talk, I will explain how these enriched
counts can be computed combinatorially using tropical geometry. I will also introduce
an arithmetic analogue of Viro's patchworking for real algebraic curves which, in some
cases, retains enough data to recover the enriched counts. This talk is based on joint
work with Hannah Markwig and Sam Payne.
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