Note: This talk will be simultaneously presented online for the Electronic Computational Homotopy Theory Seminar and live in Hylan 1106A.

Abstract: The Johnson-Wilson theories E(n) carry an action of C_2 stemming from complex conjugation. Taking fixed points yields the Real Johnson-Wilson theories, ER(n). To begin, I will survey their properties and motivate why they are interesting cohomology theories to study. I will then describe a result, joint with Kitchloo and Wilson, that presents the ER(n)-cohomology of many familiar spaces (including connective covers of BO and half of the Eilenberg MacLane spaces) as a base change of their (known) E(n)-cohomology. A key ingredient in the proof is a computation of the equivariant E(n) (or MR) cohomology of spaces with the so-called projective property. This result is interesting in its own right, as, for instance, it gives us access to certain equivariant unstable cohomology operations. If time permits, I will conclude with a brief description of a potential application to the immersion problem for real projective spaces.