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Braid closure union braid axis is ribbon concordance minimal - https://arxiv.org/abs/2607.14030
We show that a ribbon concordance minimal fibered knot K in S^3 can generate ribbon concordance minimal links by the addition of any braid closure in S^3∖K. As a corollary, we show that any link L in S^3 may be made ribbon concordance minimal by adding a single unknot linked with L. Our proofs use link Floer homology together with classical techniques.
On the Categorified Wrapping Number Conjecture (with Melissa Zhang) (Accepted) - https://arxiv.org/abs/2501.02623
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient to produce a nonzero homology class in k-grading wrap(L) on its own. This characterization primarily concerns the type of crossing resolutions abutting trivial circles.
For anyone who wishes to know more about annular Khovanov homology, here is an expository article I wrote on the subject (in particular, its sl(2,C) module structure).
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