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Refined invariants were first introduced into tropical geometry by Block and Gottsche in 2016. Since then, various authors have investigated their properties and considered several generalizations. In this talk, I will present a version of refined invariants in positive genera, incorporating contact information, which was introduced jointly with Evgenii Shustin. I will also discuss some limitations of this invariant, particularly related to real enumerative geometry, along with our proposed solution: limiting some of the point conditions to lie on the toric boundary.
This is a presentation of my Ph.D. thesis.
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