TITLE: What is the relation between the sphere spectrum and supersymmetry?
QUESTION [32 upvotes]: In this this google+ post of Urs Schreiber, he says: "Grading over the sphere spectrum is supersymmetry" and then he redirect us to the abstract idea of superalgebra (in nLab).
Are there some references (other than Kapranov and nLab) about these ideas?

REPLY [8 votes]: Like Schreiber does in his post, I would advertise the point of view developed by Sagave and Schlichtkrull in their Adv. Math 2012 paper, and used by us to study topological logarithmic geometry. Each symmetric spectrum $X$ has a graded underlying space that is really a $J$-shaped diagram $Y$. Here $J$ is a category with nerve $QS^0$, so $hocolim_J Y$ maps to $QS^0$. If $X$ is a commutative symmetric ring spectrum then $hocolim_J Y$ is an $E_{\infty}$ space over $QS^0$, i.e., it is graded over the sphere spectrum. Sagave started developing this while a postdoc in Oslo. I noted that the nerve of $J$ was not $Z$ but something with $\pi_1 = Z/2$.