Topology and Geometry Seminar

I will review some of the basic machinery used in formulating characteristic classes for coherent sheaves on complex manifolds. The main ideas go back to the fundamental work of Toledo and Tong in the 70s. A natural extension of their ideas leads to defining these invariants for higher stacks. I will showcase some of the main tools and concepts without methodically entering the subject of higher stacks, making the talk appealing to classical differential geometers. This is based on joint works with T. Tradler, M. Miller, C. Glass, and T. Hosgood.