Recently there have been some comments on our requests page:

Sander Kupers:

Maybe you could explain a bit about elliptic cohomology and topological modular forms…

and Thomas Riepe:

I would be curious about learning more on:

“… many constructions of classical algebra (eg, the theory of modular forms) are beginning to be seen to have deep homotopy-theoretic foundations.”…

Since this is somewhat related to some of my research, I have been recruited volunteered to talk about these things. The problem is that this is a ** Huge** subject and a difficult subject and there is no way to adequately represent it in blog form. On the other hand it is a beautiful subject, filled with lots of exciting tidbits. Why not give it a go anyway, right?