© | << < ? > >> | Dror Bar-Natan: Talks:
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/mel25.
Links: AKT AP APAI BG Cars DPG Ov Theta
Talk Video@YouTube (in Bonn).
Talk Video (mp4, in Bonn).
Sources: pensieve.
Abstract. "Genuinely computable" means we have computed it for random knots with over 300 crossings. "Strongest" means it separates prime knots with up to 15 crossings better than the less-computable HOMFLY-PT and Khovanov homology taken together. And hey, it's also meaningful and fun.
Continues Rozansky, Garoufalidis, Kricker, and Ohtsuki, joint with van der Veen.
URL: http://drorbn.net/mel25.
Links: APAI DD DHOEBL DK DPG Ov Scha TK ap ge24 icbs24
Handout: SGC24.html, SGC24.pdf.
Talk Video@YouTube, Toronto version.
Talk Video (mp4, Toronto version).
Sources: pensieve.