Miniseries "Floer homotopy theory" I

There has been recent interest in incorporating methods from homotopy into symplectic topology and Floer theory. We will survey some of these ideas, including Abouzaid-Blumberg's manifold-theoretic construction of the stable homotopy category, the relationship to equivariant transversality problems, and some applications.

Talk I:
I will try to motivate the subject of Floer homotopy theory, assuming essentially no background in symplectic geometry. I will highlight some key difficulties which obstructed progress in this subject for decades, and explain how some recent developments have injected new energy into the field.  (Please be warned that this talk will be essentially identical to one I gave last year at the Uni. Bonn topology seminar, and that none of the work I will discuss is due to me.)