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Zhuoming Lan

Publications and source records attributed to Zhuoming Lan.

4 recordsLinked to original sources
arXiv2026

Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold

We prove a closed-string remodeling statement for the affine binary dihedral Calabi--Yau orbifold threefold $\mathcal X=[\mathbb C^2/Γ\times\mathbb C]$, where $Γ$ is a binary dihedral subgroup of $SU(2)$. This target lies outside the toric setting of the Bouchard--Klemm--Mariño--Pasquetti remodeling conjecture: the toric mirror curve is replaced by the type-$D_l$ logarithmic Toda curve of Brini--Ma--Strachan, and the Chekhov--Eynard--Orantin topological recursion is replaced by the $\mathbb Z_2$-equivariant topological recursion of Giacchetto--Kramer--Lewański, run in the sign sector of the Toda-curve involution with the Prym kernel as its two-point input. We identify the equivariant orbifold quantum cohomology Frobenius manifold of $\mathcal X$ with the invariant Jacobian Frobenius structure of the Toda curve, and we prove that the B-model $R$-matrix, defined by regularized stationary phase, equals the A-side normalized canonical Givental--Teleman $R$-matrix on the smooth oscillatory chamber; this equality is anchored at the orbifold point through a semistable degeneration of the Toda curve. Comparing the resulting Givental--Teleman and Dunin-Barkowski--Orantin--Shadrin--Spitz graph sums then identifies, after a parity-twisted leaf substitution, the sign-sector recursion with the descendant Gromov--Witten generating functions of $\mathcal X$ in the stable range ($2g-2+n>0$ with $n>0$), and identifies the recursion free energies with the equivariant Gromov--Witten free energies of $\mathcal X$ for $g\geq2$.

math.AG↗
arXiv2025

Equivariant mirror symmetry for footballs

In this paper, we establish equivariant mirror symmetry for footballs $\mathcal{F}(m,r)$. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017], and the results by D. Tang of weighted projective lines, on [arXiv:1712.04836]. More precisely, we prove the equivalence of the $R$-matrices for A-model and B-model at large radius limit, and establish isomorphism for $R$-matrices for general radius. We further demonstrate that the graph sum of higher genus cases are the same for both models, hence establish equivariant mirror symmetry for footballs. In last two sections the large radius limit and equivariant limit are considered, resulting a generealized Bouchard-Mariño conjecture and Norbury-Scott conjecture respectively.

math.AG↗
arXiv2023

Twisted Equivariant Gromov-Witten Theory of the Classifying Space of a Finite Group

For any finite group $G$, the equivariant Gromov-Witten invariants of $[\mathbb{C}^r/G]$ can be viewed as a certain twisted Gromov-Witten invariants of the classifying stack $\mathcal{B} G$. In this paper, we use Tseng's orbifold quantum Riemann-Roch theorem to express the equivariant Gromov-Witten invariants of $[\mathbb{C}^r/G]$ as a sum over Feynman graphs, where the weight of each graph is expressed in terms of descendant integrals over moduli spaces of stable curves and representations of $G$.

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