Mingzhi Yang
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Mingzhi Yang has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Changzheng Li
School of Mathematics, Sun Yat-Sen University, Guangzhou, China
7 shared publications - Chi Zhang
Department of Mathematics, California Institute of Technology, Pasadena, Calif., U.S.A.
2 shared publications - Frank Sottile
Texas A&M University
2 shared publications - Jiayu Song
School of Mathematics, Sun Yat-Sen University, Guangzhou, China
2 shared publications - Konstanze Rietsch
Department of Mathematics, King’s College London, London, UK
2 shared publications - Vijay Ravikumar
Chennai Mathematical Institute , H1 SIPCOT IT Park, Kelambakkam , Siruseri , India
2 shared publications
Latest Publications
- Open Access
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.Open AccessAn 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. - 21 March 2025
- Published by Springer Nature in Science China Mathematics
- Vol. 68 (7) , 1523-1548
On Seidel representation in quantum K-theory of Grassmannians
- 21 March 2025
- Published by Springer Nature in Science China Mathematics
- Vol. 68 (7) , 1523-1548
On Seidel representation in quantum K-theory of Grassmannians
- Open Access
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.Open AccessA 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. - Open Access
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)).
Open AccessOn 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)).
- Open Access
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.
Open AccessOn 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.
- Open Access
A geometric proof of an equivariant Pieri rule for flag manifolds
We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.
Open AccessA geometric proof of an equivariant Pieri rule for flag manifolds
We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.
- 5 December 2018
- Published by Walter de Gruyter GmbH in Forum Mathematicum
- Vol. 31 (3) , 779-783
A geometric proof of an equivariant Pieri rule for flag manifolds
We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.
- 5 December 2018
- Published by Walter de Gruyter GmbH in Forum Mathematicum
- Vol. 31 (3) , 779-783
A geometric proof of an equivariant Pieri rule for flag manifolds
We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.