Dg-manifolds as derived manifolds

Given two smooth maps of manifolds $f:M \to L$ and $g:N \to L,$ if they are
not transverse, the fibered product $M \times_L N$ may not exist, or may
not have the correct cohomological properties. In the world of derived
manifolds, such a fibered product always exists as a smooth object,
regardless of transversality. In this talk we will describe joint work of
ours with D. Roytenberg on giving an accessible geometric model or derived
manifolds using differential graded manifolds.