A Differential Graded Approach to Derived Manifolds
Speaker: David Carchedi, Max Planck Bonn and Berkeley
Abstract: 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 expected dimension. In the world of derived manifolds, such a fibered product always exists as a smooth object, regardless of transversality. In fact, every (quasi-smooth) derived manifold is locally of this form. In this talk, we briefly explain what derived manifolds ought to be, why one should care about them, and how one can describe them. We end by explaining a bit of our joint work with Dmitry Roytenberg in which we make rigorous some ideas of Kontsevich to give a simple model for derived intersections as certain differential graded manifolds. Time permitting, we will compute some examples.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm