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We define real log curves in toric varieties and set up a well-defined counting problem for them
using the degeneration approach of Nishinou--Siebert. We then investigate the tropical analogues
of such curves to obtain a formula for their counts from the tropical description. Focusing on
the two dimensional case, we also explain how to capture Welschinger signs from a local analysis
of the degeneration, to obtain log Welschinger invariants. This is joint work with Pierrick
Bousseau.
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