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Gromov-Witten theory produces Chow and cohomology classes on the moduli of curves, and I will discuss various conjectures/speculations about their relation to the tautological ring. We develop new degeneration techniques to address these via logarithmic GW theory. Our proofs rely on several reconstruction theorems in logarithmic GW theory, which make the logarithmic degeneration formula an inductive tool to compute GW cycles via snc degenerations. Joint work with Dhruv Ranganathan
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