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Generalized Permutahedra and Schubert Calculus
We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the...
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Schubert Calculus on Newton–Okounkov Polytopes
A Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent...
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Castelnuovo–Mumford regularity of matrix Schubert varieties
Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the...
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Combinatorics of semi-toric degenerations of Schubert varieties in type C
An approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Using the polytope...
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A Positive Formula for Type A Peterson Schubert Calculus
The Peterson variety is a special case of a nilpotent Hessenberg variety, a class of subvarieties of G / B that have appeared in the study of quantum...
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On the cohomology rings of real flag manifolds: Schubert cycles
We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the...
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Classification of Schubert Galois Groups in \(\textit{Gr}\,(4,9)\)
We classify Schubert problems in the Grassmannian of 4-planes in 9-dimensional space by their Galois groups. Of the 31,806 essential Schubert...
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UNIVERSAL GRAPH SCHUBERT VARIETIES
We consider the loci of invertible linear maps f : ℂ n → (ℂ n ) * together with pairs of flags ( E • , F • ) in ℂ n such that the various restrictions f : F j →
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ħ-Deformed Schubert Calculus in Equivariant Cohomology, K-Theory, and Elliptic Cohomology
In this survey paper we review recent advances in the calculus of Chern-Schwartz-MacPherson, motivic Chern, and elliptic classes of classical...
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Probabilistic Schubert Calculus: Asymptotics
In the recent paper Bürgisser and Lerario (Journal für die reine und angewandte Mathematik (Crelles J), 2016) introduced a geometric framework for a...
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Soergel Calculus with Patches
We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We...
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Elliptic classes of Schubert varieties
We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober classes of Schubert varieties in general homogeneous spaces G / P ...
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Can We Divide Vectors?—Geometric Calculus in Science and Engineering
In this paper, we present an alternative to classic linear algebra using Clifford or geometric algebras, which allows for more geometric reasoning....
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Minuscule Schubert Calculus and the Geometric Satake Correspondence
We describe a relationship between work of Gatto, Laksov, and their collaborators on realizations of (generalized) Schubert calculus of...
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Schubert Calculus and Its Applications in Combinatorics and Representation Theory Guangzhou, China, November 2017
This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert...