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Mingzhi Yang

Publications and source records attributed to Mingzhi Yang.

8 recordsLinked to original sources
arXiv2026

Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$

We propose to study the quantum Schubert calculus for Schubert varieties, and investigate the smooth Schubert divisors X of the complete flag variety Fl_n. We provide a Borel-type ring presentation of the quantum cohomology of X. We derive the quantum Chevalley formula for X by geometric arguments. We also show that the quantum Schubert polynomials for X are the same as that for Fl_n introduced by Fomin, Gelfand and Postnikov.

math.AG↗
arXiv2025

CTourLLM: Enhancing LLMs with Chinese Tourism Knowledge

Recently, large language models (LLMs) have demonstrated their effectiveness in various natural language processing (NLP) tasks. However, the lack of tourism knowledge limits the performance of LLMs in tourist attraction presentations and travel planning. To address this challenge, we constructed a supervised fine-tuning dataset for the Chinese culture and tourism domain, named Cultour. This dataset consists of three parts: tourism knowledge base data, travelogues data, and tourism QA data. Additionally, we propose CTourLLM, a Qwen-based model supervised fine-tuned with Cultour, to improve the quality of information about attractions and travel planning. To evaluate the performance of CTourLLM, we proposed a human evaluation criterion named RRA (Relevance, Readability, Availability), and employed both automatic and human evaluation. The experimental results demonstrate that CTourLLM outperforms ChatGPT, achieving an improvement of 1.21 in BLEU-1 and 1.54 in Rouge-L, thereby validating the effectiveness of the response outcomes. Our proposed Cultour is accessible at https://github.com/mrweiqk/Cultour.

cs.CL↗
arXiv2025

An anticanonical perspective on G/P Schubert varieties

We describe a natural basis of the Cartier class group of an arbitrary Schubert variety $X_{w,P}$ in a flag variety $G/P$ of general Lie type. We then characterise when the Schubert variety is factorial/Fano, along with an explicit formula for the anticanonical line bundle in these cases. We also prove that, for Schubert varieties in simply-laced types (only), being factorial is equivalent to being $Q$-factorial, and is equivalent to the equality of the Betti numbers $b_2(X_{w,P})=b_{2\ell(w)-2}(X_{w,P})$. Finally, we give a convenient characterisation of when a simply-laced Schubert variety is Gorenstein and when it is Gorenstein Fano.

math.AG↗
arXiv2024

On Seidel representation in quantum K-theory of Grassmannians

We provide a direct proof of Seidel representation in the quantum K-theory QK(Gr(k, n)) by studying projected Gromov-Witten varieties concretely. As applications, we give an alternative proof of the K-theoretic quantum Pieri rule by Buch and Mihalcea, reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k, n)), and provide a quantum Littlewood-Richardson rule for QK(Gr(3, n)).

math.AG↗
arXiv2024

QCG-Rerank: Chunks Graph Rerank with Query Expansion in Retrieval-Augmented LLMs for Tourism Domain

Retrieval-Augmented Generation (RAG) mitigates the issue of hallucination in Large Language Models (LLMs) by integrating information retrieval techniques. However, in the tourism domain, since the query is usually brief and the content in the database is diverse, existing RAG may contain a significant amount of irrelevant or contradictory information contents after retrieval. To address this challenge, we propose the QCG-Rerank model. This model first performs an initial retrieval to obtain candidate chunks and then enhances semantics by extracting critical information to expand the original query. Next, we utilize the expanded query and candidate chunks to calculate similarity scores as the initial transition probability and construct the chunks graph. Subsequently, We iteratively compute the transition probabilities based on an initial estimate until convergence. The chunks with the highest score are selected and input into the LLMs to generate responses. We evaluate the model on Cultour, IIRC, StrategyQA, HotpotQA, SQuAD, and MuSiQue datasets. The experimental results demonstrate the effectiveness and superiority of the QCG-Rerank method.

cs.CL↗
arXiv2024

A Plücker coordinate mirror for partial flag varieties and quantum Schubert calculus

We construct a Plücker coordinate superpotential $\mathcal{F}_-$ that is mirror to a partial flag variety $\mathbb{ F}\ell(n_\bullet)$. Its Jacobi ring recovers the small quantum cohomology of $\mathbb{ F}\ell(n_\bullet)$ and we prove a folklore conjecture in mirror symmetry. Namely, we show that the eigenvalues for the action of the first Chern class $c_1(\mathbb{ F}\ell(n_\bullet))$ on quantum cohomology are equal to the critical values of $\mathcal{F}_-$. We achieve this by proving new identities in quantum Schubert calculus that are inspired by our formula for $\mathcal{F}_-$ and the mirror symmetry conjecture.

math.AG↗
arXiv2022

On Frobenius-Perron Dimension

We propose a notion of Frobenius-Perron dimension for certain free $\mathbb{Z}$-modules of infinite rank and compute it for the $\mathbb{Z}$-modules of finite dimensional complex representations of unitary groups with nonnegative dominant weights. We also provide a lower bound for the Frobenius-Perron dimension of Schubert classes in the quantum cohomology of complex Grassmannians.

math.AG↗