Talk 1. Shifted Partial Quadratics, their Pushforwards, and Signature Invariants for Tangles

Algebraic Geometry and Differential Topology Seminar, November 17, 2023.

Following a talk given at ICERM in May 2023

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.

URL: http://drorbn.net/bu23.

Handout: PQ.html, PQ.pdf.

Talk video (slides and sounds only) mp4, @Renyi.

Talk Video (version given at ICERM, also on YouTube, and perhaps a better version at the ICERM website).

Sources: pensieve.

Talk 2. Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants

Colloquium, November 27, 2023.

Following a talk given in Nara in August 2023

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.

URL: http://drorbn.net/bu23.

Links: AKT ap APAI AQDW DoPeGDO Dogma FDA Ov Scha SolvApp

Handout: Cars.html, Cars.pdf.

Talk Video (for the version given in Oaxaca; also at YouTube and at @BIRS).

After-talk writeup (for the version given in Nara): NaraTalkSummary.pdf.

Sources: pensieve.