Claudius Zibrowius

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.

The Heegaard Floer theory of a 4-ended tangle takes the form ofan immersed curve (with possibly non-trivial local system) on theboundary of the tangle minus the tangle ends. The Heegaard Floerhomology of a link can be computed as the Lagrangian...

Conway mutation is an operation on links that is notoriously difficult to detect: it preserves many link invariants such as the signature, the Alexander polynomial or, more generally, the HOMFLY polynomial. Baldwin and Levine conjectured that δ...

In the past four years, a number of immersed curve invariants have emerged in low-dimensional topology. Hanselman, Rasmussen and Watson used their immersed curve invariant for 3-manifolds with torus boundary to give an elegant proof of the fact that...