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

Expansions: A Loosely Tied Traverse from Feynman Diagrams to Quantum Algebra

Geometric, Algebraic, and Topological Methods for Quantum Field Theory,
Villa de Leyva, Colombia, July 2011

Reader's Digest: Summary.pdf.       Handout Booklet: Booklet.pdf.

Abstract. Assuming lots of luck, in six classes we'll talk about
  1. Perturbed Gaussian integration in Rn and Feynman diagrams.
  2. Chern-Simons theory, knots, holonomies and configuration space integrals.
  3. Finite type invariants, chord and Jacobi diagrams and "expansions".
  4. Drinfel'd associators and knotted trivalent graphs.
  5. w-Knotted objects and co-commutative Lie bi-algebras.
  6. My dreams on virtual knots and and quantization of Lie bi-algebras.
Each class will be closely connected to the next, yet the first and last will only be very loosely related. 		Practice. In six classes we talked about
  1. The Stonhenge story. (Slides: Stonehenge.html, video).
  2. Perturbation theory in finite dimensions and in the Chern-Simons case. (Handout: Lecture2.html and Lecture2.pdf, video).
  3. Finite type invariants, chord and Jacobi diagrams and "expansions". (Handout: Lecture3.html and Lecture3.pdf, video).
  4. Low and high algebra and knotted trivalent graphs. (Handout: Lecture4.html and Lecture4.pdf, video).
  5. Drinfel'd associators and knotted trivalent graphs. (Handout: Lecture5.html and Lecture5.pdf, video).
  6. w-Knotted objects, co-commutative Lie bi-algebras, and convolusions. (Handout: Lecture6.html and Lecture6.pdf, video).
Each class was closely connected to the next, yet the first and last were only very loosely related.

Sources: Summary.zip, Booklet.zip. Pensieve: 2011-07/.