116 citations · 183 across the 10 of their papers we have counts for
11 papers
Hypertoric Fukaya categories and categories O
Laurent Côté, Benjamin Gammage, Justin Hilburn
To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--Webster associate a category O, defined using deformation quantization (DQ) modules. It…
Hypertoric 2-categories O and symplectic duality
Benjamin Gammage, Justin Hilburn
We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift…
Twisted traces on abelian quantum Higgs and Coulomb branches
Davide Gaiotto, Justin Hilburn, Jaime Redondo-Yuste +2
We study twisted traces on the quantum Higgs branches of gauge theories, that is, the quantum Hamiltonian reductions of Weyl algebras…
Betti Tate's thesis and the trace of perverse schobers
Benjamin Gammage, Justin Hilburn
We propose a conjecture on the categorical trace of the 2-category of perverse schobers (expected to model the Fukaya-Fueter 2-category of a holomorphic symplectic space). By provi…
Perverse schobers and 3d mirror symmetry
Benjamin Gammage, Justin Hilburn, Aaron Mazel-Gee
The proposed physical duality known as 3d mirror symmetry relates the geometries of dual pairs of holomorphic symplectic stacks. It has served in recent years as a guiding principl…
Tate's thesis in the de Rham Setting
Justin Hilburn, Sam Raskin
We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind…
BFN Springer Theory
Justin Hilburn, Joel Kamnitzer, Alex Weekes
Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space…
Mirror symmetry and line operators
Tudor Dimofte, Niklas Garner, Michael Geracie +1
We study half-BPS line operators in 3d N=4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types…
Vortices and Vermas
Mathew Bullimore, Tudor Dimofte, Davide Gaiotto +2
In three-dimensional gauge theories, monopole operators create and destroy vortices. We explore this idea in the context of 3d N=4 gauge theories in the presence of an Omega-backgr…
Boundaries, Mirror Symmetry, and Symplectic Duality in 3d Gauge Theory
Mathew Bullimore, Tudor Dimofte, Davide Gaiotto +1
We introduce several families of UV boundary conditions in 3d gauge theories and study their IR images in sigma-models to the Higgs and Coulomb b…
Quadratic-linear duality and rational homotopy theory of chordal arrangements
Christin Bibby, Justin Hilburn
To any graph and smooth algebraic curve one may associate a "hypercurve" arrangement and one can study the rational homotopy theory of the complement . In the rational case…