7 citations · 9 across the 11 of their papers we have counts for
12 papers · 1 filter
On the quantum parameter in the quantum cohomology of a family of odd symplectic partial flag varieties
Connor Bean, Caleb Shank, Ryan M. Shifler
We will consider a particular family of odd symplectic partial flag varieties denoted by $\mbox{IF}$. In the quantum cohomology ring $\mbox{QH}^*(\mbox{IF})$, we will show that $q_…
Curve neighborhoods and combinatorial property for a family of odd symplectic partial flag manifolds
Connor Bean, Bradley Cruikshank, Ryan M. Shifler
Let be an odd dimensional complex vector space and $\mbox{IF}:=\mbox{IF}(1,2;E)$ be the family of odd symplectic partial flag manifold. In this paper we give a full description…
On the spectral properties of the quantum cohomology of odd quadrics
Ryan M. Shifler, Stephanie Warman
Let $H^\bullet(\mbox{OG})$ be the quantum cohomology (specialized at ) of the dimensional quadric $\mbox{OG}$. We will calculate the characteristic polynomial of the li…
Positivity determines the quantum cohomology of the odd symplectic Grassmannian of lines
Ryan M. Shifler
Let $\mbox{IG}:=\mbox{IG}(2,2n+1)$ denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring $\mbox{QH}^*(\mbox…
Minimum quantum degrees with Maya diagrams
Ryan M. Shifler
We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter that occur in a product of Schubert classes in the (small)…
Conjecture holds for some Horospherical Varieties of Picard Rank 1
Lela Bones, Garrett Fowler, Lisa Schneider +1
Property for an arbitrary complex, Fano manifold , is a statement about the eigenvalues of the linear operator obtained from the quantum multiplication of the anti…
Curve neighborhoods of Schubert Varieties in the odd symplectic Grassmannian
Clelia Pech, Ryan M. Shifler
Let $\mbox{IG}(k,2n+1)$ be the odd symplectic Grassmannian. It is a quasi-ho\-mo\-ge\-neous space with homogeneous-like behavior. A very limited description of curve neighborhoods…
Galkin's lower bound conjecture holds for the Grassmannian
La'Tier Evans, Lisa Schneider, Ryan M. Shifler +2
Let Gr be the Grassmannian. The quantum multiplication by the first Chern class induces an endomorphism of the finite-dimensional vector spac…
Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C
Ryan M. Shifler, Camron Withrow
We give a formula in terms of Young diagrams to calculate the minimum positive integer such that appears in the quantum product of two Schubert classes for the submaximal…
On Frobenius-Perron Dimension
Changzheng Li, Ryan M. Shifler, Mingzhi Yang +1
We propose a notion of Frobenius-Perron dimension for certain free -modules of infinite rank and compute it for the -modules of finite dimensional complex r…
Conjecture holds for the odd symplectic Grassmannian
Changzheng Li, Leonardo C. Mihalcea, Ryan Shifler
Let be the odd-symplectic Grassmannian. Property , introduced by Galkin, Golyshev and Iritani for arbitrary complex, Fano manifolds , is a st…
Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian
Leonardo C. Mihalcea, Ryan M. Shifler
The odd symplectic Grassmannian parametrizes dimensional subspaces of which are isotropic with respect to a general (nec…