publications

2026

1. Siebert’s Formula for Virtual Pullbacks

   Xuanchun Lu, and Rachel Webb

   Sep 2026

   Abs DOI

   For a DM-type morphism of algebraic stacks \(f \colon X \to Y\)with a relative perfect obstruction theory \(\mathbbE \to \mathbbL_X/Y\)having a global resolution, we give a formula for the induced virtual pullback in terms of \(\mathbbE\)and \(f\). We apply our formula to prove functoriality properties of the virtual fundamental class in Gromov-Witten theory.

2. Bulk-Deformed Enumerative Mirror Symmetry for Toric Fano Surfaces

   Xuanchun Lu

   Sep 2026

   Abs DOI

   We prove a version of genus-0 mirror symmetry for toric Fano surfaces at the level of big quantum cohomology. The mirror Landau-Ginzburg model \((\checkX, W_∞)\)of such a surface \(X\)can be defined in terms of counts of Maslov index two tropical or holomorphic discs with bulk insertions. While these mirror LG models are not well-defined, the Jacobian ring \(\operatorname\mathsfJac(W_∞)\)of the superpotential \(W_∞\)is well-defined. We show that \(\operatorname\mathsfJac(W_∞)\)is isomorphic over the Novikov base to the big quantum cohomology of \(X\)using tropical methods, providing a purely algebraic analogue of the cobordism argument used in works of Fukaya-Oh-Ohta-Ono.