Abstract: I will talk about Adams spectral sequences that compute the homotopy groups of the tensor products of BP<n>’s (truncated Brown—Peterson spectra) and endomorphism rings of BP<n>’s. For tensor products of BP<n>’s, the Adams spectral sequences are well-understood, but their homotopy types are largely unknown. For endomorphism rings of BP<n>’s, much less is known about the spectral sequences, but I will talk about their relations to other uniqueness problems, such as infinite loop space structures of Wilson spaces.
