This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical
Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures …

The concept of orbifolds should unify differential geometry with equivariant homotopy theory,
so that orbifold cohomology should unify differential cohomology with proper equivariant …

We survey the general theory of groupoids, groupoid actions, groupoid principal bundles,
and various kinds of morphisms between groupoids in the framework of categories with …

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is
given by the source vertical tangent bundle restricted to the identity bisection. Its sections …

We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale
symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer …

In this paper, we study diffeological spaces as certain kinds of discrete simplicial presheaves
on the site of cartesian spaces with the coverage of good open covers. The Čech model …

Inertia orbifolds homotopy-quotiented by rotation of geometric loops play a fundamental role
not only in ordinary cyclic cohomology, but more recently in constructions of equivariant Tate …

We describe various equivalent ways of associating to an orbifold, or more generally a
higher étale differentiable stack, a weak homotopy type. Some of these ways extend to …

We discuss how local prequantum field theories with boundaries can be described in terms
of n-fold correspondence diagrams in the infinity-topos of smooth stacks equipped with …

In this thesis, we employ simplicial methods to study actions, principal bundles, and
bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher …