Brooke Shipley (Purdue University)
bshipley@math.purdue.edu
I will discuss a thickening of the category of rings inspired by stable homotopy theory. Here rings in the classical sense correspond to ordinary cohomology theories, whereas "rings up to homotopy" correspond to generalized cohomology theories. Although these generalized rings were defined twenty years ago, recent progress has allowed the wholesale transport of algebraic methods into this domain. Applications of this new form of algebra will be discussed, including new derived equivalences of differential graded rings and algebraic models analogous to Quillen's model for rational homotopy theory.