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In the last few years, researchers have observed a phenomenon in several different
moduli problems in logarithmic and tropical geometry. The phenomenon is a form of
non-transversality of intersections that arises in many natural geometric problems.
The examples relate to degeneration formulas for enumerative invariants, the geometry
of the double ramification cycle, and the Gromov-Witten theory of infinite root
stacks. Tropical geometry, and more specifically the combinatorics of extended (or
compactified) tropicalizations, seems to be very good at detecting and controlling
these extraneous components. After giving an overview of these ideas, I will share a
formalism that explains what is going on here, and how it leads to a conjecture about
certain moduli spaces of higher dimensional varieties. Joint work with Thibault
Poiret, and related to prior work with Battistella, Molcho, Nabijou.
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