In the present paper, we review the progress of the project of the classification and
construction of invariant differential operators for non-compact, semisimple Lie groups. Our …

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 …

We develop a general framework for the description of anomalies using extended functorial
field theories extending previous work by Freed and Monnier. In this framework, anomalies …

We study discrete symmetries of Dijkgraaf–Witten theories and their gauging in the
framework of (extended) functorial quantum field theory. Non-abelian group cohomology is …

In the present paper, we review the progress of the project of the classification and
construction of invariant differential operators for non-compact, semisimple Lie groups. Our …

This paper is devoted to the construction of differential geometric invariants for the
classification of “quaternionic” vector bundles. Provided that the base space is a smooth …

The topology of electrons on a lattice subject to a periodic driving is captured by the three-
dimensional winding number of the propagator that describes time evolution within a cycle …

We analyze topological invariants, in particular Z 2 invariants, which characterize time
reversal invariant topological insulators, in the framework of index theory and K-theory. After …