| #
|
Week of...
|
Notes and Links
|
| 1
|
Jan 6
|
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)
|
| 2
|
Jan 13
|
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.
|
| 3
|
Jan 20
|
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.
Class Photo.
|
| 4
|
Jan 27
|
Homework Assignment 3.
Monday: Chord diagrams and weight systems.
Wednesday: Swaddling maps and framings, general configuration space integrals.
Friday: Some analysis of  .
|
| 5
|
Feb 3
|
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, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d^{-1}}
, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d^\ast}
.
|
| 6
|
Feb 10
|
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.
|
| R
|
Feb 17
|
Reading Week.
|
| 7
|
Feb 24
|
Monday: A review of Lie algebras.
Wednesday: Graph cohomology and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Omega_{dR}^\ast(\Gamma)}
.
Friday: More on Feynman diagrams, beginning of gauge theory.
From Gaussian Integration to Feynman Diagrams (PDF).
|
| 8
|
Mar 3
|
Homework Assignment 6 (PDF)
Monday: Lie algebraic weight systems.
Wednesday: Graph cohomology and the construction of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_0}
.
Graph Cohomology and Configuration Space Integrals (PDF)
Friday: Gauge invariance, Chern-Simons, holonomies.
Mar 9 is the last day to drop this class.
|
| 9
|
Mar 10
|
Homework Assignment 7 (PDF)
Monday: The Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle gl(N)}
weight system.
Wednesday: The universal property, hidden faces.
Friday: Insolubility of the quintic, naive expectations for CS perturbation theory.
|
| 10
|
Mar 17
|
Homework Assignment 8 (PDF)
Monday:  and PBW.
Wednesday: The anomaly.
Friday: Faddeev-Popov, part I.
Gaussian Integration, Determinants, Feynman Diagrams (PDF).
|
| 11
|
Mar 24
|
Homework Assignment 9 (PDF)
Monday: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathcal A}}
is a bi-algebra.
Wednesday: Understanding and fixing the anomaly.
Friday: class cancelled.
|
| 12
|
Mar 31
|
Monday, Wednesday: class cancelled.
Friday: A Monday class: back to expansions.
|
| E
|
Apr 7
|
Monday: A Friday class on what we mostly didn't have time to do.
|
Add your name / see who's in!
|
| Dror's Notebook
|
|
|
Algebraic Knot Theory
Department of Mathematics, University of Toronto, Spring 2014
Agenda. Three courses on just one theorem: With Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal K}
the set of knots and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal A}
something naturally associated to knots and quite related to Lie algebras, there exists an expansion Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z\colon\mathcal K\to\mathcal A}
.
Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.
Classes. Mondays and Wednesdays at 11:10-12:00 and Fridays at 10:10 at Bahen 6180.
Full Description (PDF).
