Stabilization of the Khovanov Homotopy Type of Torus Links

Both the Jones polynomial and its categorification, the Khovanov homology, are known to stabilize for torus links T(n,m) as m goes to infinity. In recent work, Robert Lipshitz and Sucharit Sarkar constructed the Khovanov homotopy type of a link, a spectrum whose reduced cohomology recovers the Khovanov homology of the link. In this talk I will discuss stability of these homotopy types for torus links as m goes to infinity. If time permits, I will also discuss more recent work regarding a tail as n to goes to infinity (similar to the tail of the colored Jones polynomial), as well as a definition for a colored Khovanov homotopy type for links.