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 …

We promote geometric prequantization to higher geometry (higher stacks), where a
prequantization is given by a higher principal connection (a higher gerbe with connection) …

Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that
are equipped with compatible homological vector fields. These new objects are closely …

We introduce quasi-symplectic groupoids and explain their relation with momentum map
theories. This approach enables us to unify into a single framework various momentum map …

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 …

These notes discuss various aspect of the``representation theory''of Poisson manifolds, with
focus on Morita equivalence and Picard groups. We give a brief introduction to Poisson …

The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of
conjugacy classes in a certain open subset SL˜(2, R)+ of the universal cover of SL (2, R). We …

We start by describing the relationship between the classi-cal prequantization condition and
the integrability of a certain Lie algebroid associated to the problem and use this to give a …

Let G be a compact, simply connected Lie group. We develop a 'quantization functor'from
prequantized quasi-Hamiltonian G-spaces (M, ω, Φ) at level k to the fusion ring (Verlinde …

We define-shifted and-shifted contact structures on differentiable stacks, thus laying the
foundations of shifted Contact Geometry. As a side result we show that the kernel of a …