Θ: 4😀4😢

A Panorama of Quantum Topology - Recent Progress in Quantum Algebra, Low-Dimensional Topology, and Mathematical Physics, Banff, July 20-24, 2026.

Abstract. Recently, in September 2025, Roland van der Veen and myself released a paper titled "A Fast 😀, Strong 😀, Topologically Meaningful 😀, and Fun 😀 Knot Invariant" (arXiv:2509.18456). More recently, in January 2025 in Les Diablerets (https://drorbn.net/ld26), I gave a talk in which I suggested 27 homework tasks related to that same invariant $\Theta$ (plus a bonus task).

Today, after a brief review, I'll talk a bit more about just 4 of those tasks:

Figure out the relationship of $\Theta$ with Chern Simons theory.
Complete the discussion of the relationship of $\Theta$ with $sl_3$.
Find formulas for $\Theta$ corresponding to other presentations of the Alexander module.
Fully understand $\Theta$-like formulas and their non-uniqueness (i.e., clean the mess).

URL: http://drorbn.net/ba26.

Links: APAI DD DHOEBL Ov Theta icbs24 ld26 pi

Handout: 4S4F.html, 4S4F.pdf.

Talk Video@YouTube.

Talk Video (mp4).

Sources: pensieve.