© | AI | << < ? > >> | Dror Bar-Natan: Talks:
Abstract. When you intersect half-dimensional cycles in 4D or higher, you get a count. In 2D, half-dimensional cycles can be replaced by paths and they and their intersections carry homotopical information. After inquiring why we should care, we ponder if this intersection theory has a graded model, and an expansion, much as the Taylor series is an expansion of smooth functions into their graded model, the space of power series.
The tentative affirmative answer uses Drinfeld associators and/or solutions of the KV equations, and makes drunken port calls at "emergent" knots in 3D which barely know knottedness, at truly knotted knots in 4D, at a theory of convolutions on finite dimensional Lie groups and algebras, and maybe in the theory of quantum groups. God was having a good laugh when she threw all this at us without a user's manual.
URL: http://drorbn.net/agtw26.
Talk Video@YouTube.
Talk Video (mp4).
Sources: pensieve.
Backup Plan: Repeat my talk from July in Banff, Θ: 4😀4😢.