Dear All, The following preprint is now available on the arXiv at: http://arxiv.org/abs/1312.2204. D. Carchedi, "Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi" Abstract: We develop a framework for modeling higher orbifolds and Deligne-Mumford stacks as infinity topoi equipped with a structure sheaf. This framework is general enough to apply to differential topology, classical algebraic geometry, and also derived and spectral variants of the latter. The general set up is to start with a class of geometric objects, which are to be thought of as local models, and then to use them as building blocks in much the same way one builds manifolds out of Euclidean spaces, or schemes out of affine schemes. When starting with Euclidean smooth manifolds, this results in a theory of higher orbifolds and higher \'etale differentiable stacks. When applied to affine schemes, it produces Lurie's higher Deligne-Mumford stacks, and more generally, when applied to derived affine schemes or spectral affine schemes, it produces Lurie's derived Deligne-Mumford stacks and spectral Deligne-Mumford stacks. We give categorical characterizations of the resulting geometric objects in the general setting, as well as their functors of points, which are far reaching generalizations of previous results of the author about \'etale stacks. These specialize to a new characterization of classical Deligne-Mumford stacks which extends to the derived and spectral setting as well. In the differentiable setting, this characterization shows that there is a natural correspondence between n-dimensional higher \'etale differentiable stacks (generalized higher orbifolds), and classical fields for n-dimensional field theories, in the sense of Freed and Teleman. The underpinning idea behind this work is the following phenomenon, which seems to really be a phenomenon in higher topos theory: If one starts with a collection of local models (modeled as structured infinity topoi), then the higher category of higher sheaves over the site of local models and local homeomorphisms is equivalent to the higher category of "higher orbifolds" constructed out of these local models and their respective local homeomorphisms. Kind Regards, David Carchedi [For admin and other information see: http://www.mta.ca/~cat-dist/ ]