Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively
hop on a discrete tessellation of two-dimensional (2D) hyperbolic space, a non-Euclidean …

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum
electrodynamics and electric-circuit networks, where particles coherently hop on a discrete …

Hyperbolic lattices underlie a new form of quantum matter with potential applications to
quantum computing and simulation and which, to date, have been engineered artificially. A …

In this paper, we consider the wild nonabelian Hodge correspondence for principal G-
bundles on curves, where G is a connected complex reductive group. We establish the …

We develop a geometric framework, based on the classical theory of fibre bundles, to
characterize the cohomological nature of a large class of synchronization-type problems in …

This survey provides an introduction to basic questions and techniques surrounding the
topology of the moduli space of stable Higgs bundles on a Riemann surface. Through …

In this article, we study the Hitchin morphism over a smooth projective variety. The Hitchin
morphism is a map from the moduli space of Higgs bundles to the Hitchin base, which in …

We provide a general method for constructing moduli stacks whose points are diagrams of
vector bundles over a fixed base, indexed by a fixed simplicial set--that is, quiver bundles of …

This paper is a survey aimed on the introduction of non-Abelian Hodge theory that gives the
correspondence between flat bundles and Higgs bundles. We will also introduce some …

Ordinarily, quiver varieties are constructed as moduli spaces of quiver representations in the
category of vector spaces. It is also natural to consider quiver representations in a richer …