© | << < ? > >> | Dror Bar-Natan: Talks:

Within Grothendieck-Teichmüller, Kashiwara-Vergne and MZVs, at the University of Geneva.

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

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

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.