Khovanov homology and Conway mutation

What has homological mirror symmetry ever done for you?  I will give my personal answer to that question and discuss joint work in progress with Liam Watson and Artem Kotelskiy concerning the behaviour of Khovanov homology under Conway mutation.  
 

Claudius was a postdoctoral fellow at UBC working with Liam Watson from 2018 to 2021. He is currently a professor in low-dimensional topology at the mathematics department of Ruhr-University Bochum and holds a Starting Grant from the European Research Council.