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Dror Bar-Natan: Talks:
SMS 2013, Physics and Mathematics of Link Homology,
CRM, Montreal, June 24 - July 5, 2013

Three Talks in Montreal

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Handout: kh.pdf, kh.html, AnnotatedKhProgram.pdf, kh2.html.
Videos. talk I, talk II.
Real time notes. talk I, talk II.
Sources: sources.zip, pensieve.

1. A Quick Introduction to Khovanov Homology, I

2. A Quick Introduction to Khovanov Homology, II

Abstract. As appropriate for a relic from the past, I will tell the Kauffman bracket story of the Jones polynomial as Kauffman told it in 1987, then the Khovanov homology story as Khovanov told it in 1999, and finally the "local Khovanov homology" story as I understood it in 2003 (with perhaps a word about alternating tangles). At the end of my two talks you will understand what is a "Jones homology", how to generalize it to tangles and to cobordisms between tangles, and why it is computable relatively efficiently. But we will say nothing about more modern stuff - the Rasmussen invariant, Alexander and HOMFLYPT knot homologies, and the categorification of sl2 and other Lie algebras.

Handout: beta.pdf, beta.html. Video. talk III. Real time notes. talk III.
Sources: sources.zip, pensieve.

3. Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial

Abstract. I will define "meta-groups" and explain how one specific meta-group, which in itself is a "meta-bicrossed-product", gives rise to an "ultimate Alexander invariant" of tangles, that contains the Alexander polynomial (multivariable, if you wish), has extremely good composition properties, is evaluated in a topologically meaningful way, and is least-wasteful in a computational sense. If you believe in categorification, that's a wonderful playground.

See also my likewise-titled paper with Sam Selmani.