Abstract: The symplectic fiber sum construction is one of the few surgery technique available to construct new symplectic manifolds out of olds ones. The goal of the talk is to explain the construction and, if time permits, to give some applications .

Abstract: Various model structures for the category of pro objects in simplicial sheaves will be displayed. These structures extend the standard homotopy theory for simplicial sheaves in the sense that their weak equivalences are locally defined. They also extend known results for simplicial sets, and thus, for example, give a common framework for modern simplicial sheaf homotopy theory and classical \'etale homotopy theory. One or more applications will be discussed.