Searcharxiv⌕ Search

arXiv subjects

Zekai Yu

Publications and source records attributed to Zekai Yu.

7 recordsLinked to original sources
arXiv2026

Family Floer SYZ mirror algorithm for the Grassmannian $Gr(2,4)$

We give an explicit non-archimedean SYZ construction for the Landau-Ginzburg mirror of $Gr(2,4)$. This work is complementary to the approach of Hong-Kim-Lau \cite{hong2023immersed} to SYZ mirror symmetry for Grassmannians, while we focus on a more concrete fibration-level realization of the SYZ picture. Starting from a Lagrangian fibration on the A-side, we explicitly construct a non-archimedean analytic mirror fibration inside the Berkovich analytification of the Langlands dual Grassmannian on the B-side. We show that the two fibrations have identical smooth and singular loci and induce the same integral affine structure on the smooth locus. Moreover, the natural disk-counting Landau-Ginzburg superpotential agrees with the Marsh-Rietsch superpotential. While the construction is guided by the family Floer viewpoint, the proof proceeds mainly through explicit geometric constructions and does not rely on Floer-theoretic arguments. Thus, the Langlands-dual mirror and its superpotential are realized explicitly within a single framework, providing concrete geometric evidence for the SYZ principle.

math.AG↗
arXiv2026

ParaTool: Shifting Tool Representations from Context to Parameters

Tool calling extends large language models (LLMs) by enabling grounded interaction with external executable interfaces, thereby supporting environment-coupled problem solving. However, mainstream in-context learning (ICL) approaches typically incorporate detailed tool documentation and usage examples directly into the context. This results in substantial inference overhead and heightened risks of hallucination as the context length grows. Conversely, while tuning-based methods improve general tool-calling capabilities, they often fail to effectively internalize the specific details of previously seen tools, thereby retaining a dependency on in-context documentation. To address these limitations, we propose ParaTool, a framework that projects each tool into a dedicated, loadable set of parameters. By equipping a dynamic integration of these parameterized tools, the LLM can perform tool calling without relying on in-context documents or examples. Specifically, our approach consists of three stages: (1) parametric tool pre-training encapsulates the knowledge of different tools into independent parameter modules; (2) soft tool selection employs a gating network to dynamically weigh and aggregate relevant tool parameters; and (3) parametric tool fine-tuning jointly updates tool parameters to align the training and inference processes. Experiments on Stable ToolBench and BFCL demonstrate that ParaTool significantly outperforms strong ICL-based baselines, achieving superior performance while reducing computational complexity.

cs.AI↗
arXiv2024

On holographic duals of certain isolated weighted Gorenstein cDV singularities

We employ a novel approach,based on homological mirror symmetry for Landau-Ginzburg models,to demonstrate the non-existence of crepant resolutions for certain weighted homogeneous Gorenstein compound Du Val singularities.Physically,this implies that such singularities cannot serve as holographic backgrounds for four dimensional N=1 superconformal quiver gauge theories realized on the worldvolume of a large number of D3 branes placed at the singular locus.This is confirmed by enumerating all consistent quiver gauge theories.

hep-th↗
arXiv2024

GraphTeam: Facilitating Large Language Model-based Graph Analysis via Multi-Agent Collaboration

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

cs.AI↗
arXiv2023

Genus 2 Seiberg-Witten curves for rank 2 N=4 superYang-Mills theories

We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N=4 superYang-Mills theories using the automorphism twist approach. The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the $so(5) \simeq sp(4)$ superYang-Mills theory the genus-2 curve corresponds to. We also compare the curves to earlier constructions of Seiberg-Witten curves for these theories as spectral curves of integrable systems. These spectral curves have genus greater than the rank, and so only give a Coulomb branch geometry upon projection to a sublattice of the homology lattice of the curves. We show how to determine the correct sublattice projection, and find that the integrable system curves do not apply to our theories.

hep-th↗
arXiv2023

Hyperelliptic families and 4d $\mathcal{N}=2$ SCFT

We classify four dimensional $\mathcal{N}=2$ SCFTs whose Seiberg-Witten (SW) geometries can be written as hyperelliptic families. By using special K\"ahler condition of SW geometry, we reduce the problem to one parameter quasi-homogeneous hyperelliptic families $y^2=f(x,t)$. The classification is given by further demanding that the complex algebraic surface defined by $y^2=f(x,t)$ has an isolated singularity. We then write down the full SW geometry by looking at mini-versal deformations of the one parameter family, and the SW differential is also written down. The detailed physical data for these theories are found by matching the theory with other known construction. Our solutions recover the known rank one and rank two results, and give some infinite sequences valid at arbitrary ranks. We also studied $Z_2$ quotient of above hyperelliptic families which give rise to $B$ type and $D$ type conformal gauge theory, and further generalizations.

hep-th↗