| Résume | I will discuss recent and ongoing work with Davesh Maulik that explains how Gromov-Witten invariants behave under simple normal crossings degenerations. The main outcome of the study is that if a projective X undergoes a simple normal crossings degeneration, the Gromov-Witten theory of X is determined, via universal formulas, by the Gromov-Witten theory of the strata of the degeneration. Although the proof proceeds via logarithmic geometry, the statement involves only traditional Gromov-Witten cycles. I will discuss applications of this to a conjecture of Levine and Pandharipande, concerning the relationship between Gromov-Witten theory and the cohomology of the moduli space of curves. |
