$C_{2}$-Equivariant analogues of Brown-Gitler spectra and their applications

Short introductory lectures.

In recent work, Guchuan Li, Sarah Peterson, and I have constructed models for $C_{2}$-equivariant analogues of the classical integral Brown-Gitler spectra. In this talk, I will start by introducing the classical Brown-Gitler spectra and discussing some of their applications. Then I will discuss the $C_{2}$-equivariant applications we are currently studying.