Justin Campbell (Brandeis)

In their 1997 paper on semi-infinite flags, Feigin, Finkelberg, Kuznetsov, and Mirković constructed a remarkable action of the Langlands dual Lie algebra on the intersection cohomology of the space of quasimaps into a flag variety. They conjectured that this representation is tilting and explained how this is equivalent to a conjectural spectral description of the representation. I’ll sketch a proof of this conjecture, which is joint work in progress with Andreas Hayash. Our strategy is to construct a purely local version of the FFKM action and then use chiral homology to pass from local to global.