In this talk, we shall exhibit explicit formulas for the odd Chern character map.

Following Chapter 2 of the HoTT Book, I will present the main properties of the Identity Type.

We will discuss the convex floating body method of extending Blaschke's affine surface area measure to all convex bodies. We will then introduce the Fefferman hypersurface area measure on the boundary of a strongly pseudoconvex domain. This measure transforms well under biholomorphisms, and we will discuss why this can be useful. Taking tube domains as the motivating case, we will propose a method for extending this measure to general pseudoconvex domains.

This talk is a leisurely introduction to spectra, symmetric spectra and cup products in stable homotopy theory. Ring spectra are discussed as examples, in various contexts.