Prof. Dan Freed, University of Texas at Austin
The classifying space of a group has different incarnations in topology and algebraic geometry, for example. In joint work with Mike Hopkins we introduce a differential geometric manifestation whose de Rham complex consists precisely of the Chern-Weil forms. This differential geometric BG also provides a natural home for equivariant de Rham theory. The definitions and proofs use abstract homotopy theory. We illustrate the effectiveness of this BG in implementing the equivariance → families maneuver in differential geometric contexts.