Semi-infinite t-structures via hyperbolic localization

For any nice enough scheme with an action of the multiplicative group it is possible to define a t-structure on a certain category of monodromic D-modules using hyperbolic localization. I will discuss the construction of these t-structures as well as an application to geometric representation theory. Specifically, I will explain how the semi-infinite IC sheaf associated to a semisimple group arises as an intermediate extension in this t-structure for Drinfeld's Zastava spaces.