the main aim of this talk is proposing a definition of +1-shifted contact structure on a differentiable stack thus laying the foundations of +1-shifted contact geometry. As a side result I will show that the kernel of a multiplicative 1-form on a Lie groupoid (might not exist as a vector bundle of Lie groupoids but) it always exists as a vector bundle of differentiable stacks and it carries a stacky version of the curvature of a distribution. Prequantum bundles over +1-shifted symplectic groupoids provide examples of +1-shifted contact structures. Time permitting, I will also discuss 0-shifted contact structures which, in some aspects, are surprisingly more complicated than +1-shifted ones. This is joint work with A. Maglio and A. Tortorella.
