Khovanov multicurves are linear

Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09 Meeting ID: 682 8556 4037 Passcode: 636252

For a given invariant the geography problem asks for a characterization of values the invariant attains. For example, it is well understood which Laurent polynomials arise as the Alexander polynomial of a knot. By contrast, very little is known about which values the Jones polynomial takes. And the situation is at least as bad for Khovanov homology. So it is a little surprising that the Khovanov homology of a tangle, which can be framed in terms of immersed curves in the 4-punctured sphere, satisfies rather strict geography—the invariants are “linear”. My talk, which is based on joint work with Artem Kotelskiy and Claudius Zibrowius, will explain what “linear” means, and tell part of the story of how this comes up.