Categorification of Link Homologies via Homotopy Types

Links appear in many areas of mathematics, and the study of their invariants is a well-established problem. In particular, it is an interesting question if and how invariants can be recovered from higher invariant structures that enhance them and possibly provide more information.
In this expository talk, we will present one example of link invariant (the triply-graded link homology by Khovanov and Rozansky) and one possible categorification via equivariant homotopy types. This is based on the work by Kitchloo (https://arxiv.org/abs/1910.07443 and https://arxiv.org/abs/1910.07444).
If time permits, we will also briefly discuss how this construction can be obtained from the categorical setting provided by traces and bicategories.