E-infinity ring spectra and Hopf invariant one elements Seminar

At the prime 2, the sequence of Hopf invariant one elements $2,\eta,\nu,\sigma$ appear as attaching maps in low skeleta of the classifying spaces $BO,BSO,BSpin,BO\langle 8\rangle$, and their associated Thom spectra, and in fact these agree with skeleta of $H\mathbb{Z}/2,H\mathbb{Z},kO, tmf$. Applying the $Q(-)$ construction and Thomifying leads to interesting E-infinity ring spectra. I'll discuss these and show how to use them to prove some results on the homology of Thom spectra.