7 papers
Grassmannian quantum cohomology in the infinite limit and total positivity
Ines Chung-Halpern, Konstanze Rietsch
The theory of total positivity was shown by Lusztig to be intrinsically linked to the canonical basis with its positivity properties. When we restrict ourselves to studying total p…
Totally positive Toeplitz matrices: classical and modern
Konstanze Rietsch
By a theorem of Edrei, an infinite, normalised totally nonnegative upper-triangular Toeplitz matrix is determined by a pair of nonnegative parameter sequences, the `Schoenberg para…
Tropical Toeplitz matrices and parametrisations
Konstanze Rietsch
The set of infinite upper-triangular totally positive Toeplitz matrices has a classical parametrisation proved by Edrei et al and originally conjectured by Schoenberg, that involve…
The tropical critical point and mirror symmetry
Jamie Judd, Konstanze Rietsch
Call a Laurent polynomial `complete' if its Newton polytope is full-dimensional with zero in its interior. We show that if is any complete Laurent polynomial with coefficie…
A superpotential for Grassmannian Schubert varieties
Konstanze Rietsch, Lauren Williams
While mirror symmetry for flag varieties and Grassmannians has been extensively studied, Schubert varieties in the Grassmannian are singular, and hence standard mirror symmetry sta…
An anticanonical perspective on G/P Schubert varieties
Changzheng Li, Konstanze Rietsch, Mingzhi Yang
We describe a natural basis of the Cartier class group of an arbitrary Schubert variety in a flag variety of general Lie type. We then characterise when the Schuber…