arXiv subjects

Benjamin Zhou

Publications and source records attributed to Benjamin Zhou.

5 recordsLinked to original sources

arXiv2026

Open-closed duality in higher genus and winding

Let $X$ be a toric Fano surface. Let $\pi: \widehat{X} \rightarrow X$ be a toric blow up at a point. We use the Topological Vertex [AKMV] to prove a higher genus, higher winding, open-closed duality between the toric Calabi-Yau 3-folds $K_X, K_{\widehat{X}}$. For $g \geq 0, w \geq 1$, we show the equality $n_g(K_{\widehat{X}}, \pi^*\beta - wC) = (-1)^g N_{g, (w)}^{LMOV}(K_X/L, \beta)$, where $n_g(K_{\widehat{X}}, \pi^*\beta - wC)$ is the genus-$g$, Gopakumar-Vafa invariant of $K_{\widehat{X}}$ in curve class $\pi^*\beta-wC$, where $\beta \in H_2(X, \mathbb{Z})$ and $C$ is the exceptional curve, and $N_{g, (w)}^{LMOV}(K_X/L, \beta)$ is the genus-$g$, LMOV invariant of an outer Aganagic-Vafa brane $L \subset K_X$ in class $\beta$ and representation $(w)$, or the Young Tableau of a single row with $w$ boxes.

math.AG↗

arXiv2026

InFlux++: Real and Synthetic Data for Estimating Dynamic Camera Intrinsics

Camera intrinsics are vital for recovering 3D structure from 2D video. However, most 3D algorithms assume fixed intrinsics throughout a video, an assumption that often fails for real-world in-the-wild videos. Consequently, estimating per-frame intrinsics from RGB images is critical for making 3D methods robust to videos with dynamic intrinsics. InFlux previously advanced this research direction by establishing the first real-world benchmark with per-frame ground truth intrinsics for dynamic intrinsics videos. Nevertheless, existing methods remain inaccurate due to two obstacles: (i) training data is scarce and lacks intrinsics diversity; and (ii) benchmarks, including InFlux, have limited scene and camera motion diversity, making it difficult to properly evaluate methods. To address both gaps, we present InFlux++, consisting of two components. InFlux++ Synth is a large-scale procedurally generated synthetic video dataset with 441K+ annotated frames from 1841 high-resolution videos, providing accurate per-frame ground truth intrinsics for training dynamic intrinsics prediction models; a subset also includes per-frame pose, depth, and normals. The videos feature rich intrinsics diversity through changes in camera zoom and focus, as well as dynamic objects and realistic rendering effects such as lens distortion and defocus blur. InFlux++ Real is a large-scale real-world benchmark that extends InFlux with 514K+ newly captured frames across 334 high-resolution videos, spanning a wider range of scenes and camera motions. Finetuning existing intrinsics prediction methods on InFlux++ Synth consistently improves focal length estimation across both InFlux++ Real and InFlux, suggesting that synthetic supervision is promising for RGB-based intrinsics prediction. For the dataset, benchmark, code, videos, submission instructions, and live leaderboard, please visit https://influx.cs.princeton.edu/.

cs.CV↗

arXiv2025

Tropical super Gromov-Witten invariants

We show that super Gromov-Witten invariants can be defined and computed by methods of tropical geometry. When the target is a point, the super invariants are descendant invariants on the moduli space of curves, which can be computed tropically. When the target is a convex, toric variety $X$, we describe a procedure to compute the tropical Euler class of the SUSY normal bundle $\overline{N}_{n, \beta}$ on $\overline{\mathcal{M}}_{0,n}(X, \beta)$, assuming it is locally tropicalizable in the sense of [CG], [CGM]. Then, we define the tropical, genus-0, $n$-marked, super Gromov-Witten invariant of $X$, and compute an example. This gives a tropical interpretation of super Gromov-Witten invariants of convex, toric varieties.

math.AG↗

arXiv2025

Higher genus Gromov-Witten invariants from projective bundles on smooth log Calabi-Yau pairs

Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z := \mathbb{P}(K_X \oplus \mathcal{O}_X)$, using the degeneration formula for stable log maps [KLR]. We evaluate an invariant in the degeneration using the relationship between $q$-refined tropical curve counting and logarithmic Gromov-Witten theory with $\lambda_g$-insertion [Bou]. As a corollary, we use flops to prove a blow up formula for higher genus invariants of $Z$. Additionally assuming $X$ is toric, we prove an all-genus correspondence between open invariants of an outer Aganagic-Vafa brane $L \subset K_X$ and closed invariants of $Z$ that generalizes a genus-0 open-closed equality of [Cha] to all-genus, by using an argument in [GRZZ].

math.AG↗

arXiv2025

Enumerative Geometry of Quantum Periods

We interpret the $q$-refined theta function $\vartheta_1$ of a log Calabi-Yau surface $(\mathbb{P},E)$ as a natural $q$-refinement of the open mirror map, defined by quantum periods of mirror curves for outer Aganagic-Vafa branes on the local Calabi-Yau $K_{\mathbb{P}}$. The series coefficients are all-genus logarithmic two-point invariants, directly extending the relation found in [GRZ]. Yet we find an explicit discrepancy at higher genus in the relation to open Gromov-Witten invariants of the Aganagic-Vafa brane. Using a degeneration argument, we express the difference in terms of relative invariants of an elliptic curve. With $\pi: \widehat{\mathbb{P}} \rightarrow \mathbb{P}$ the toric blow up of a point, we use the Topological Vertex [AKMV] to show a correspondence between open invariants of $K_{\mathbb{P}}$ and closed invariants of $K_{\widehat{\mathbb{P}}}$ generalizing a variant of [CLLT][LLW] to arbitrary genus and winding. We also equate winding-1, open-BPS invariants with closed Gopakumar-Vafa invariants.

math.AG↗