77 citations · 179 across the 13 of their papers we have counts for
16 papers
Contact isotopies in the coherent-constructible correspondence
Jishnu Bose, Harold Williams
The coherent-constructible correspondence is a realization of toric mirror symmetry in which the A-side is modeled by constructible sheaves on . This paper provides a geometri…
Differential operators on the base affine space of and quantized Coulomb branches
Tom Gannon, Harold Williams
We show that the algebra of differential operators on the base affine space of is the quantized Coulomb branch of a certain 3d quiver gau…
Canonical bases for Coulomb branches of 4d gauge theories
Sabin Cautis, Harold Williams
We construct and study a nonstandard t-structure on the derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima space of triples ,…
Tamely presented morphisms and coherent pullback
Sabin Cautis, Harold Williams
We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and m…
Ind-geometric stacks
Sabin Cautis, Harold Williams
We develop the theory of ind-geometric stacks, in particular their coherent and ind-coherent sheaf theory. This provides a convenient framework for working with equivariant sheaves…
Kasteleyn operators from mirror symmetry
David Treumann, Harold Williams, Eric Zaslow
Given a consistent bipartite graph in with a complex-valued edge weighting we show the following two constructions are the same. The first is to form the Ka…
Cluster theory of the coherent Satake category
Sabin Cautis, Harold Williams
We study the category of G(O)-equivariant perverse coherent sheaves on the affine Grassmannian of G. This coherent Satake category is not semisimple and its convolution product is…
Affine cluster monomials are generalized minors
Dylan Rupel, Salvatore Stella, Harold Williams
We study the realization of acyclic cluster algebras as coordinate rings of Coxeter double Bruhat cells in Kac-Moody groups. We prove that all cluster monomials with g-vector lying…
On Generalized Minors and Quiver Representations
Dylan Rupel, Salvatore Stella, Harold Williams
The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, definin…
On the combinatorics of exact Lagrangian surfaces
Vivek Shende, David Treumann, Harold Williams
We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing on…
Cluster varieties from Legendrian knots
Vivek Shende, David Treumann, Harold Williams +1
Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link.…
The greedy basis equals the theta basis
Man Wai Cheung, Mark Gross, Greg Muller +4
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
Toda Systems, Cluster Characters, and Spectral Networks
Harold Williams
We show that the Hamiltonians of the open relativistic Toda system are elements of the generic basis of a cluster algebra, and in particular are cluster characters of nonrigid repr…
Q-Systems, Factorization Dynamics, and the Twist Automorphism
Harold Williams
We provide a concrete realization of the cluster algebras associated with Q-systems as amalgamations of cluster structures on double Bruhat cells in simple algebraic groups. For no…
Cluster Ensembles and Kac-Moody Groups
Harold Williams
We study the relationship between two sets of coordinates on a double Bruhat cell, the cluster variables introduced by Berenstein, Fomin, and Zelevinsky and the $\CX$-coordinates d…
Double Bruhat Cells in Kac-Moody Groups and Integrable Systems
Harold Williams
We construct a family of integrable Hamiltonian systems generalizing the relativistic periodic Toda lattice, which is recovered as a special case. The phase spaces of these systems…