Conway mutation, Khovanov homology, and Fukaya categories

by Dr Claudius Zibrowius (Universität Regensburg)

Tuesday 3 May 2022, 17:00 → 18:00 Europe/Berlin

H4 (Geom)

Zoom Link:
https://uni-hamburg.zoom.us/j/63441868540?pwd=N2xjUktiLy9hOE9nTjFCMUx3UXFPdz09

Abstract:
Knot theory is currently undergoing the same transformative process
that algebraic topology went through about 80 years earlier:  Just like
Noether (and others) in the 1920s replaced the Euler and Betti numbers
by homology groups, Khovanov, Ozsváth-Szabó, and Rasmussen around 20
years ago initiated the programme of categorification in low-
dimensional topology, replacing basic numerical and polynomial knot
invariants by knot homology groups.

In recent years, it has become clear that relative versions of these
new homology theories can often be understood via Fukaya categories of
simple surfaces.  I will discuss why this new perspective is useful,
focussing on a very concrete motivating example, namely the behaviour
of Khovanov homology under Conway mutation.  This is joint work in
progress with Liam Watson and Artem Kotelskiy.