10 citations · 14 across the 11 of their papers we have counts for
13 papers
Affine Springer fiber and the small quantum group
Roman Bezrukavnikov, Pablo Boixeda Alvarez, Michael McBreen +1
We find a new geometric incarnation for the principal block in the category of modules over a quantum group at a root of unity, realizing it as a full subcategory of microsheaves o…
The Hamiltonian reduction of hypertoric mirror symmetry
Michael McBreen, Vivek Shende, Peng Zhou
We give a `Fukaya category commutes with reduction' theorem for the Hamiltonian torus action on a multiplicative hypertoric variety.
Non-abelian Hodge moduli spaces and homogeneous affine Springer fibers
Roman Bezrukavnikov, Pablo Boixeda Alvarez, Michael McBreen +1
Starting from a homogeneous affine Springer fiber , we construct three moduli spaces that correspond to the Dolbeault, de Rham and Betti aspects of a hypothetical Simpson cor…
Elliptic stable envelopes and hypertoric loop spaces
Michael McBreen, Artan Sheshmani, Shing-Tung Yau
This paper relates the elliptic stable envelopes of a hypertoric variety with the K-theoretic stable envelopes of the loop hypertoric space, . It thus…
Twisted Quasimaps and Symplectic Duality for Hypertoric Spaces
Michael McBreen, Artan Sheshmani, Shing-Tung Yau
We study moduli spaces of twisted quasimaps to a hypertoric variety , arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametris…
Hypertoric Hitchin systems and Kirchhoff polynomials
Michael Groechenig, Michael McBreen
We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-analytic counterparts were defined by Hausel-Proudfoot. These are algebraic completely integrable…
Deletion-contraction triangles for Hausel-Proudfoot varieties
Zsuzsanna Dancso, Michael McBreen, Vivek Shende
To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively like moduli of local systems on a Riemann surface, and moduli of Higgs bundles…
Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
Benjamin Gammage, Michael McBreen, Ben Webster
In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories…
The quantum Hikita conjecture
Joel Kamnitzer, Michael McBreen, Nicholas Proudfoot
The Hikita conjecture relates the coordinate ring of a conical symplectic singularity to the cohomology ring of a symplectic resolution of the dual conical symplectic singularity.…
Homological Mirror Symmetry for Hypertoric Varieties I
Michael McBreen, Ben Webster
We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertori…
Intersection cohomology and quantum cohomology of conical symplectic resolutions
Michael McBreen, Nicholas Proudfoot
For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this con…
Quantum Cohomology of Hypertoric Varieties
Michael B. McBreen, Daniel K. Shenfeld
We give a complete description of the equivariant quantum cohomology ring of any smooth hypertoric variety, and find a mirror formula for the quantum differential equation.
Excited States of U(1) Lattice Gauge Theory from Monte Carlo Hamiltonian
A. Hosseinizadeh, G. Melkonyan, H. Kröger +2
We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of latt…