arXiv subjects

Mingyuan Hu

Publications and source records attributed to Mingyuan Hu.

7 recordsLinked to original sources

arXiv2026

Mirror Counts of Spectral Curves

Given a convex lattice polygon $\Delta\subset \mathbb R^2$, let $N_\Delta$ be the count of rational, nodal curves in the linear system of the ample line bundle $L_\Delta$ on the toric variety $\mathbb P_\Delta$ defined by $\Delta$, having fixed intersection with the toric boundary. We show that the relative Jacobian of the linear system defines an integrable system that has a mirror dual in the language of constructible sheaves on a two-torus microsupported on a Legendrian link. In this setting, we define the dual counting problem using an analogue of rulings of Legendrian links in three-space, then prove equivalence with $N_\Delta$. We perform calculations of $N_\Delta$ in several examples using constructible methods, tropical curve counting, and localization in logarithmic Gromov-Witten theory to demonstrate the equality of the different approaches. Moreover, the rulings give rise to a stratification of the moduli of constructible sheaves. We conjecture that this ruling decomposition recovers the refined tropical invariants of Block-G\"ottsche, and hence encodes higher-genus logarithmic Gromov--Witten invariants, by a theorem of Bousseau.

math.SG↗

arXiv2026

Mirror symmetry for the Painlev\'e character varieties

We establish a homological mirror theorem for the 4-manifolds arising as moduli of (irregular) rank two local systems on the projective line. Specifically, we prove that the Fukaya category of a moduli of such local systems with generic microlocal monodromy at punctures is equivalent to the category of coherent sheaves on the minimal resolution of the corresponding moduli of local systems with trivial microlocal monodromy.

math.SG↗

arXiv2026

Crystal-Field Symmetry Constraints in Layered Honeycomb ErBr$_3$

Crystal-field symmetry restricts the ground-state Kramers doublet of ErBr$_3$ to one of two classes. We show that the compressed octahedral environment selects the class with $\langle \psi_\pm | J^{\pm} | \psi_\mp \rangle = 0$, suppressing the lowest-order $J^{\pm}$-mediated exchange. Thermodynamic measurements reveal two zero-field anomalies at 0.375 and 0.200~K. Under an in-plane magnetic field, the thermodynamic response separates into a phase boundary and a broader crossover line. Inelastic neutron scattering measurements at 2 K reveal no well-defined low-energy dispersive magnetic modes. These results connect the ground-state symmetry with the field-dependent thermodynamic response of ErBr$_3$, providing a microscopic starting point for understanding its low-energy magnetic behavior.

cond-mat.str-el↗

arXiv2025

Skein-valued mirror curves for toric CY3 strips

For a smooth semi-projective toric Calabi-Yau 3-fold containing no compact surface, we show the count of all-genus holomorphic curves with boundary on a single Aganagic-Vafa brane is annihilated by a skein-valued quantization of the mirror curve, and that this determines the count. We give explicit expressions for the equation and its solution.

math.SG↗

arXiv2025

A Proof of the Pentagon Relation for Skeins

In \cite{HSZ23}, with Gus Schrader and Eric Zaslow we developed a skein-theoretic version of cluster theory, and made a conjecture on the pentagon relation for the skein dilogarithm. Here we give a topological proof of this conjecture. Combining \cite{MS21} and \cite{BCMN23}, we get a surjection from the skein algebra $\mathrm{Sk}^+(T - D)$ to the positive part of the elliptic Hall algebra $\mathcal{E}_{q, t}^+$. Hence our pentagon relation generalizes the ones in \cite{Z23} and \cite{GM19}.

math.QA↗

arXiv2025

Visible-Thermal Tiny Object Detection: A Benchmark Dataset and Baselines

Small object detection (SOD) has been a longstanding yet challenging task for decades, with numerous datasets and algorithms being developed. However, they mainly focus on either visible or thermal modality, while visible-thermal (RGBT) bimodality is rarely explored. Although some RGBT datasets have been developed recently, the insufficient quantity, limited category, misaligned images and large target size cannot provide an impartial benchmark to evaluate multi-category visible-thermal small object detection (RGBT SOD) algorithms. In this paper, we build the first large-scale benchmark with high diversity for RGBT SOD (namely RGBT-Tiny), including 115 paired sequences, 93K frames and 1.2M manual annotations. RGBT-Tiny contains abundant targets (7 categories) and high-diversity scenes (8 types that cover different illumination and density variations). Note that, over 81% of targets are smaller than 16x16, and we provide paired bounding box annotations with tracking ID to offer an extremely challenging benchmark with wide-range applications, such as RGBT fusion, detection and tracking. In addition, we propose a scale adaptive fitness (SAFit) measure that exhibits high robustness on both small and large targets. The proposed SAFit can provide reasonable performance evaluation and promote detection performance. Based on the proposed RGBT-Tiny dataset and SAFit measure, extensive evaluations have been conducted, including 23 recent state-of-the-art algorithms that cover four different types (i.e., visible generic detection, visible SOD, thermal SOD and RGBT object detection). Project is available at https://github.com/XinyiYing/RGBT-Tiny.

cs.CV↗

arXiv2023

Skeins, clusters and wavefunctions

In previous work of the second- and third-named authors with Linhui Shen, cluster theory was used to construct wavefunctions for branes in threespace and conjecturally relate them to open Gromov-Witten invariants. This was done by defining a quantum Lagrangian subvariety of a quantum cluster variety, and mutating a simple solution to the defining equations in a distinguished seed. In this paper, we extend the construction to incorporate the skein-theoretic approach to open Gromov-Witten theory of Ekholm-Shende. In particular, we define a skein-theoretic version of cluster theory, including the groupoid of seeds and mutations and a skein-theoretic version of the quantum dilogarithm. We prove a pentagon relation in the skein of the closed torus in this context, and give strong evidence that its analogue holds for arbitrary surfaces. We propose face relations satisfied by the skein-theoretic wavefunction, prove their invariance under mutations, and show their solution is unique. We define a skein version of framings in the story, and use the novel cluster structure to compute wavefunctions in several examples. The skein approach incorporates moduli spaces of sheaves of higher microlocal rank and their quantizations.

math.SG↗