||Notes and Links
||About This Class (PDF). |
Monday: Course introduction, knots and Reidemeister moves, knot colourings.
Tricolourability without Diagrams
Wednesday: The Gauss linking number combinatorially and as an integral.
Friday: The Schroedinger equation and path integrals.
Friday Introduction (the quantum pendulum)
||Homework Assignment 1. |
Monday: The Kauffman bracket and the Jones polynomial.
Wednesday: Self-linking using swaddling.
Friday: Euler-Lagrange problems, Gaussian integration, volumes of spheres.
||Homework Assignment 2. |
Monday: The definition of finite-type and some examples.
Wednesday: The self-linking number and framings.
Friday: Integrating a polynomial times a Gaussian.
||Homework Assignment 3. |
Monday: Chord diagrams and weight systems.
Wednesday: Swaddling maps and framings, general configuration space integrals.
Friday: Some analysis of .
||Homework Assignment 4. |
Monday: 4T, the Fundamental Theorem and universal finite type invariants.
The Fulton-MacPherson Compactification (PDF).
Wednesday: The Fulton-MacPherson Compactification, Part I.
Friday: More on pushforwards, , and .
||Homework Assignment 5. |
Monday: The bracket-rise theorem and the invariance principle.
Wednesday: The Fulton-MacPherson Compactification, Part II.
Friday: Gauge fixing, the beginning of Feynman diagrams.
|| Monday: A review of Lie algebras. |
Wednesday: Graph cohomology and .
Friday: More on Feynman diagrams, beginning of gauge theory.
From Gaussian Integration to Feynman Diagrams (PDF).
||Homework Assignment 6 (PDF) |
Monday: Lie algebraic weight systems.
Wednesday: Graph cohomology and the construction of .
Graph Cohomology and Configuration Space Integrals (PDF)
Friday: Gauge invariance, Chern-Simons, holonomies.
Mar 9 is the last day to drop this class.
||Homework Assignment 7 (PDF) |
Monday: The weight system.
Wednesday: The universal property, hidden faces.
Friday: Insolubility of the quintic, naive expectations for CS perturbation theory.
||Homework Assignment 8 (PDF) |
Monday: and PBW.
Wednesday: The anomaly.
Friday: Faddeev-Popov, part I.
Gaussian Integration, Determinants, Feynman Diagrams (PDF).
||Homework Assignment 9 (PDF) |
Monday: is a bi-algebra.
Wednesday: Understanding and fixing the anomaly.
Friday: class cancelled.
||Monday, Wednesday: class cancelled. |
Friday: A Monday class: back to expansions.
|| Monday: A Friday class on what we mostly didn't have time to do.
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Algebraic Knot Theory
Department of Mathematics, University of Toronto, Spring 2014
Agenda. Three courses on just one theorem: With the set of knots and something naturally associated to knots and quite related to Lie algebras, there exists an expansion .
Instructor: Dror Bar-Natan, email@example.com, Bahen 6178, 416-946-5438. Office hours: by appointment.
Classes. Mondays, Wednesdays, and Fridays at 10:10-11:00; Mondays and Fridays at Bahen 6180 but Wednesdays at Huron 1018. There will also be a "HW meeting", covering no new material, on Fridays at 6:10PM at Bahen 6180.
About This Class (PDF).