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Dror Bar-Natan:
Talks:

# Some Feynman Diagrams in Algebra

**Abstract.** I will explain how the computation of compositions of
maps of a certain natural class, from one polynomial ring into another,
naturally leads to a certain composition operation of quadratics and to
Feynman diagrams. I will also explain, with very little detail, how this
is used in the construction of some very well-behaved poly-time computable
knot polynomials.

Joint work with Roland van der Veen.

**Handout:**
FDA.html,
FDA.pdf,
FDA.png.

**Talk Video**.

**Links:**
Ov
akt
hm
sl2

**Sources:** pensieve.

### Aborted earlier plan:

## Everything around $sl_{2+}^\epsilon$ is **DoPeGDO**. So what?

**Abstract.** I'll explain what "everything around" means:
classical and quantum $m$, $\Delta$, $S$, $tr$, $R$, $C$, and $\theta$,
as well as $P$, $\Phi$, $J$, ${\mathbb D}$, and more, and all of their
compositions. What **DoPeGDO** means: the category of Docile Perturbed
Gaussian Differential Operators. And what $sl_{2+}^\epsilon$ 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.