Higher Structure Conferences Carchedi (changes)

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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.