Everything around sl(2+,\eps) is DoPeGDO. So what?

Macquarie University, October 23, 2019.

Abstract. I'll explain what "everything around" means: the classical and quantum product, co-product, antipode, trace, R-matrix, cuap, and Cartan involution, as well as the dual pairing, the associator, the twist element, the dequantizator, and more, and all of their compositions. What DoPeGDO means: the category of Docile Perturbed Gaussian Differential Operators. And what sl(2+,\eps) means: a solvable approximation of the semi-simple Lie algebra sl(2).

Knot theorists should rejoice because all this leads to very powerful and well-behaved poly-time-computable knot invariants. Quantum algebraists should rejoice because it's a realistic playground for testing complicated equations and theories.

This is joint work with Roland van der Veen and continues work by Rozansky and Overbay.

Handout: DoPeGDO.html, DoPeGDO.pdf, DoPeGDO.png.

See videos at DaNang-1905 and at CRM-1907.

Links: NCSU Ov Za atoms cm engine akt kiw kt oa objects qa talks

Sources: pensieve.