William Slofstra
YOU?
Author Swipe
View article: Operator solutions of linear systems and small cancellation
Operator solutions of linear systems and small cancellation Open
We show that if a graph has minimum vertex degree at least d and girth at\nleast g, where (d, g) is (3, 6) or (4, 4), then the incidence system of the\ngraph has a (possibly infinite-dimensional) quantum solution over\n$\\mathbb{Z}_p$ for …
View article: Positivity is undecidable in tensor products of free algebras
Positivity is undecidable in tensor products of free algebras Open
It is well known that an element of the algebra of noncommutative *-polynomials is positive in all *-representations if and only if it is a sum of squares. This provides an effective way to determine if a given *-polynomial is positive, by…
View article: Satisfiability problems and algebras of boolean constraint system games
Satisfiability problems and algebras of boolean constraint system games Open
Mermin and Peres showed that there are boolean constraint systems (BCSs) which are not satisfiable, but which are satisfiable with quantum observables. This has led to a burgeoning theory of quantum satisfiability for constraint systems, c…
View article: The isomorphism problem for Schubert varieties
The isomorphism problem for Schubert varieties Open
Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. We give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are isomo…
View article: Enumerating Staircase Diagrams and Smooth Schubert Varieties over type $E$ Dynkin Diagrams
Enumerating Staircase Diagrams and Smooth Schubert Varieties over type $E$ Dynkin Diagrams Open
We enumerate the number of staircase diagrams over classically finite $E$-type Dynkin diagrams, extending the work of Richmond and Slofstra (Staircase Diagrams and Enumeration of smooth Schubert varieties) and completing the enumeration of…
View article: Enumerating Staircase Diagrams and Smooth Schubert Varieties over type\n $E$ Dynkin Diagrams
Enumerating Staircase Diagrams and Smooth Schubert Varieties over type\n $E$ Dynkin Diagrams Open
We enumerate the number of staircase diagrams over classically finite\n$E$-type Dynkin diagrams, extending the work of Richmond and Slofstra\n(Staircase Diagrams and Enumeration of smooth Schubert varieties) and\ncompleting the enumeration…
View article: Staircase diagrams and the enumeration of smooth Schubert varieties
Staircase diagrams and the enumeration of smooth Schubert varieties Open
In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert varieties are in bijection with a new combi…
View article: Parabolic double cosets in Coxeter groups
Parabolic double cosets in Coxeter groups Open
Parabolic subgroups WI of Coxeter systems (W,S) and their ordinary and double cosets W/WI and WI\W/WJ appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmet…
View article: Complexity Lower Bounds for Computing the Approximately-Commuting Operator Value of Non-Local Games to High Precision
Complexity Lower Bounds for Computing the Approximately-Commuting Operator Value of Non-Local Games to High Precision Open
We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is NP-complete to decide whether the classical value of a non-local game is 1 or 1- epsilon, promised that one of t…
View article: A group with at least subexponential hyperlinear profile
A group with at least subexponential hyperlinear profile Open
The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least $\exp(1/ε^{k})…
View article: Smooth Schubert varieties in the affine flag variety of type $\tilde{A}$
Smooth Schubert varieties in the affine flag variety of type $\tilde{A}$ Open
We show that every smooth Schubert variety of affine type $\tilde{A}$ is an iterated fibre bundle of Grassmannians, extending an analogous result by Ryan and Wolper for Schubert varieties of finite type $A$. As a consequence, we finish a c…
View article: The cotangent bundle of a cominuscule Grassmanian
The cotangent bundle of a cominuscule Grassmanian Open
A theorem of the first author states that the cotangent bundle of the type A Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety.We extend this result to cotangent b…
View article: The Cotangent Bundle of a Cominuscule Grassmannian
The Cotangent Bundle of a Cominuscule Grassmannian Open
A theorem of the first author states that the cotangent bundle of the type $A$ Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety. We extend this result to cotangen…