(1-)Stacks were invented by Deligne and Mumford in the '60s in order for moduli "spaces" of curves to exist as geometric objects in some reasonable sense. However, there are classification problems that require an even further generalization of the concept of geometric space for their moduli "spaces" to exist as such. In hopefully no more than two talks I will try to give the basic intuition and machinery of these so-called higher stacks, along with some examples.

In the interest of time I will assume some basic knowledge of Grothendieck (pre)topologies and model categories. A general intuition of (infty,1)-categories would be useful to attendees.