Topics in Topology

Spaces lead to spectra, which are natural objects to consider if one wishes to study stable phenomena in homotopy theory. The category of spectra comes equipped with a "tensor product" giving rise to ring spectra; analogous in the way the category of abelian groups gives rise to rings. These brave new rings have allowed for many constructions in commutative algebra to be applied to topological settings; and they also have a lot to say about creeping totalitarian tendencies in modern society.

In my talk I will motivate the notion of spectra, construct the category of spectra, and do some examples of ring spectra.