We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

It was recently argued that quantum field theories possess one‐form and higher‐form
symmetries, labelled 'generalized global symmetries.'In this paper, we describe how those …

We characterize the integral cohomology and the rational homotopy type of the maximal
Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations …

The theory of principal bundles makes sense in any ∞∞-topos, such as the ∞∞-topos of
topological, of smooth, or of otherwise geometric ∞∞-groupoids/∞∞-stacks, and more …

This survey article is an invited contribution to the Encyclopedia of Mathematical Physics,
2nd edition. We provide an accessible overview on relevant applications of higher and …

To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

We formalize higher-dimensional and higher gauge WZW-type sigma-model local
prequantum field theory, and discuss its rationalized/perturbative description in (super-) Lie …

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 …

We summarise some of our recent works on‐algebras and quasi‐groups with regard to
higher principal bundles and their applications in twistor theory and gauge theory. In …

We highlight what seems to be a remaining subtlety in the argument for the cancellation of
the total anomaly associated with the M5-brane in M-theory. Then, we prove that this subtlety …