Solvable Approximations of the Quantum $sl_2$ Portfolio

Matemale, April 2018

Our Main Theorem (loosely stated). Everything that matters in the quantum $sl_2$ portfolio can be continuously expressed in terms of docile perturbaed Gaussians using solvable approximations.

Our Main Points.

What's the "quantum $sl_2$ portfolio"?
What in it "matters" and why? (the most important question)
What's "solvable approximation"? What's "continuously"?
What are "docile perturbed Gaussians"?
Why do they matter? (2^nd most important)
How proven? (docile)
How implemented? (sacred; the work of unsung heros)
Some context and background.
What's next?

Joint work with Roland van der Veen.

Handout: Matemale-1804-1.html, Matemale-1804-2.html, Matemale-1804.pdf, Matemale-1804.png.

Links: AlexDemo FullImp Iowa K17 KBH NCSU Ov SL2Portfolio SS Za ZipBindDemo

Sources: pensieve.

Videos of All Talks.

Monday April 23.

Dror Bar-Natan on Solvable Approximations of the Quantum $sl_2$ Portfolio (1).
Virginie Bonnier on Definitions of the Alexander Polynomial.
Jean-Marc Hok on Definitions of the Alexander Polynomial.
Konstantinis Karvounis on Definition of the Alexander Polynomial Using Burau.
Fathi Ben Aribi on Defining the Alexander, Episodes VIII and IX.

Tuesday April 24.

Roland van der Veen on Hopf Algebras and Snarls.
Sonny Willetts on Yang Baxter Equations and Monoidal Categories.
Sjabbo Schaveling on Quantum Enveloping Algebras and Lie Bi-Algebras.
Martin Palmer-Anghel on Vassiliev Invariants the Coloured Jones Function and the Melvin-Morton-Rozansky Conjecture.

Wednesday April 25.

Dror Bar-Natan on Solvable Approximations of the Quantum $sl_2$ Portfolio (2).
Roland van der Veen on The Multiplication Formula in the Drinfel'd Double.

Thursday April 26.

Jules Martel on Braid Representations and Kohno's Theorem (1).
Jules Martel on Braid Representations and Kohno's Theorem (2).
Dror Bar-Natan on Solvable Approximations of the Quantum $sl_2$ Portfolio (3).
Roland van der Veen on Explicit Isomorphisms and Solvability.
Ajinkya Kulkarni on Representation Theory of $U_q sl(2)$, Quantization of an Infinitesimal Symmetric Category and Drinfel'd Associators.

Friday April 27.

Cristina Palmer-Anghel on Topological Formula for the Loop Expansion of the Coloured Jones Polynomial.
Roland van der Veen on Zip, Bind, and Double.
Dror Bar-Natan - Discussion.