Abstract. Reporting on joint work with Roland van der Veen, I'll tell you some stories about $\rho_1$, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. $\rho_1$ was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.
Links: AKT ap APAI AQDW DoPeGDO Dogma FDA J Ov Scha SolvApp
Handout: Cars.html, Cars.pdf.
After-talk writeup (for the version given in Nara): NaraTalkSummary.pdf.
Talk Video (also at YouTube, also @BIRS).
Abstract. Following a general discussion of the computation of zombians of unfinished columbaria (with examples), I will tell you about my recent joint work with Jessica Liu on what we feel is the "textbook" extension of knot signatures to tangles, which for unknown reasons, is not in any of the textbooks that we know.
Handout: PQ.html, PQ.pdf.
Talk Video (also on YouTube, and perhaps a better version at ICERM).