We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its
mathematical foundations with an emphasis on higher algebraic structures and classical …

We continue our study of zero-dimensional field theories in which the fields take values in a
strong homotopy Lie algebra. In the first part, we review in detail how higher Chern–Simons …

We develop a description of higher gauge theory with higher groupoids as gauge structure
from first principles. This approach captures ordinary gauge theories and gauged sigma …

Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-
connections to differential cocycles whose volume holonomy is the corresponding Chern …

We argue that the relevant higher gauge group for the non-abelian generalization of the self-
dual string equation is the string 2-group. We then derive the corresponding equations of …

These are notes for four lectures on higher structures in M-theory as presented at workshops
at the Erwin Schrödinger Institute and Tohoku University. The first lecture gives an overview …

A bstract The G/G WZW model results from the WZW-model by a standard procedure of
gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted …

We study some graded geometric constructions appearing naturally in the context of gauge
theories. Inspired by a known relation of gauging with equivariant cohomology we …

There is a well-established procedure of assigning a strong homotopy Lie algebra of local
observables to a multisymplectic manifold which can be regarded as part of a categorified …

In this article, we give a concise summary of‐algebras viewed in terms of Chevalley–
Eilenberg algebras, Weil algebras and invariant polynomials and their use in defining …