MAT 2000 Project Proposal

Brave New Rings (with John Rognes)

For applications to geometry and topology it is often necessary to work with a generalized notion of a ring, called a structured ring spectrum or a brave new ring. One project is to learn one of the modern definitions of this notion and to construct in full detail some of the most interesting examples, such as the sphere spectrum, bordism spectra and the new form of ordinary rings. Then one may go on to prove some of their basic properties. Such a project will provide an excellent basis for a Master's degree in algebraic topology. Prerequisites: knowing what a ring, a vector space and a topological space are. Some references:

A survey talk by John Rognes:

An untitled book project by Stefan Schwede:

Proceedings from an Oberwolfach workshop: