UC Berkeley

This thesis is a conglomerate of several results in algebraic topology united by the common thread of taking seriously the idea that geometric considerations can be useful for proving algebraic results in the field of chromatic homotopy theory. These results include a geometric construction of equivariant elliptic cohomology at the Tate curve, abstract derivations of the dual Steenrod algebras at all primes, and geometric presentations of higher algebraic structures.