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Enumerative period integrals of Landau-Ginzburg models

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KA2W03 - Mathematical physics: algebraic cycles, strings and amplitudes

For a del Pezzo surface Y with smooth anticanonical divisor D, form the log K3 surface (Y,D). Relative cycles in (Y,D) combine into a variation problem that computes the genus 0 log Gromov-Witten invariants of maximal tangency of (Y,D). Passing through the Gross-Siebert mirror construction, there is an equivalent variation problem in terms of period integrals on the mirror Landau-Ginzburg model. We prove that these periods compute the log Gromov-Witten invariants of (Y,D). This joint work with Siebert and Ruddat solves a conjecture by N. Takahashi from 2001.

This talk is part of the Isaac Newton Institute Seminar Series series.

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