We put the theory of interacting topological crystalline phases on a systematic footing. These
are topological phases protected by space-group symmetries. Our central tool is an …

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 …

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 …

Despite the plausible necessity of topological protection for realizing scalable quantum
computers, the conceptual underpinnings of topological quantum logic gates had arguably …

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 …

There are fundamental open problems in the precise global nature of RR-field tadpole
cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5 …

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 consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the
image of the non-abelian Chern character map from the non-abelian generalized …