At first sight, the definitions of Heegaard Floer homology and Khovanov homology seem quite different, but there are many surprising analogies between them. The strategy of finding and exploiting these similarities has been around for almost 20 years now, but remains relevant. I’ll describe some past successes of this method together with some prospects for future research
This talk was part of the conference "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021