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Dror Bar-Natan:
Talks:

# Two Talks in Geneva, August 2024

## Talk I: Secondary Operations, Emergent Knots, and the Goldman-Turaev Lie Algebra

On Tuesday August 13.
**Abstract.** I will explain what are "secondary operations" (that's
a technical term, not an insult) and explain how and why I like to see
the Goldman bracket and the Turaev co-bracket as secondary operations on spaces of
"emergent knots" ("emergent" is in fact a mild insult).

**My Notes:** EmergentNotes.pdf.

**Talk
Video**@YouTube.

**Talk Video** (mp4).

## Talk II: Knot Invariants from Finite Dimensional Integration

On Thursday August 15.
**Abstract.** For the purpose of today, an "I-Type Knot Invariant"
is a knot invariant computed from a knot diagram by integrating the
exponential of a *pertubed Gaussian* Lagrangian which is a sum
over the features of that diagram (crossings, edges, faces) of locally
defined quantities, over a product of finite dimensional spaces associated
to those same features.

**Q.** Are there any such things?

**A.** Yes.

**Q.** Are they any good?

**A.** They are the strongest we know per CPU cycle, and are excellent in other
ways too.

**Q.** Didn't Witten do that back in 1988 with path integrals?

**A.** No. His constructions are infinite dimensional and far from rigorous.

**Q.** But integrals belong in analysis!

**A.** Ours only use squeaky-clean algebra.

**URL:** http://drorbn.net/ge24.

**Links:**
AKT
AP
APAI
BG
Cars
DK
DPG
Ov

**Handout:**
IType.html,
IType.pdf.

**Talk
Video**@YouTube (Beijing version).

**Talk Video** (mp4)
(Geneva version).

**Sources:** pensieve.