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 …

We study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We
show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of …

We propose a global geometric framework which allows one to encode a natural non-
perturbative generalisation of usual Batalin-Vilkovisky (BV-) theory. Namely, we construct a …

We provide a general, homotopy-theoretic definition of string group models within an∞-
category of smooth spaces and present new smooth models for the string group. Here, a …

We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for
gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We …

We suggest a geometric approach to quantisation of the twisted Poisson structure
underlying the dynamics of charged particles in fields of generic smooth distributions of …

This is a mostly self-contained survey article about bundle gerbes and some of their recent
applications in geometry, field theory, and quantisation. We cover the definition of bundle …

In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes
contribute topological terms to the action of worldsheets of both open and closed strings. We …

We examine certain nonassociative deformations of quantum mechanics and gravity in three
dimensions related to the dynamics of electrons in uniform distributions of magnetic charge …

Extended Field Theories include Double Field Theory (DFT) and Exceptional Field Theory,
which are respectively the T-and U-duality covariant formulations of the supergravity limit of …