Foundations of Derived Differential Geometry. Part 2MPIM

by Dave Carchedi (George Mason University)

Wednesday Feb 4, 2026, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Higher Differential Geometry Seminar

Derived differential geometry is the C-infinity counterpart of derived algebraic geometry. The role of affine schemes is played by derived manifolds, which are geometric objects constructed by taking iterative fibered products of smooth manifolds. This can be made precise via a simple universal property for the infinity category of derived manifolds, proposed by myself and Pelle Steffens. Steffens and I prove moreover that derived manifolds are equivalent to affine derived schemes of finite presentation with respect to the algebraic theory of C-infinity rings. At the same time, we have constructed a concrete model for derived manifolds using differential graded manifolds, which have various applications to mathematical physics. In this talk, we will explain the above results precisely, as well as sketching some of the main ideas behind the proofs.