I’ll describe a method for producing the complex cobordism theory MU as a coherent associative ring spectrum by attaching coherently associative cells along certain classes in Ravenel’s X(n) spectra that appear to be related to chromatic height. These classes are determined geometrically, but there is some indeterminacy in choosing them without a geometric understanding of MU. However, this indeterminacy disappears after localizing at any prime. As such, this construction can be thought of as a canonical p-local algebraic construction of MU. If there is time I will describe a generalization of this construction which produces MU as an E_n-ring via repeated cell attachments for any n, although in this case I don’t know of any meaningful description of the classes or of the E_n-ring spectra that interpolate between the sphere spectrum and MU.

There will also be a pretalk in the same location from 2 to 3.