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Week of...
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Notes and Links
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| 1
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Jan 6
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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)
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| 2
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Jan 13
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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.
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| 3
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Jan 20
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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.
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| 4
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Jan 27
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Homework Assignment 3.
Monday: Chord diagrams and weight systems.
Wednesday: Swaddling maps and framings, general configuration space integrals.
Friday: Some analysis of [math]\displaystyle{ d^{-1} }[/math].
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| 5
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Feb 3
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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, [math]\displaystyle{ d^{-1} }[/math], and [math]\displaystyle{ d^\ast }[/math].
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| 6
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Feb 10
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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.
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| R
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Feb 17
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Reading Week.
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| 7
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Feb 24
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Monday: A review of Lie algebras.
Wednesday: Graph cohomology and [math]\displaystyle{ \Omega_{dR}^\ast(\Gamma) }[/math].
Friday: More on Feynman diagrams, beginning of gauge theory.
From Gaussian Integration to Feynman Diagrams (PDF).
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| 8
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Mar 3
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Homework Assignment 6 (PDF)
Monday: Lie algebraic weight systems.
Wednesday: Graph cohomology and the construction of [math]\displaystyle{ Z_0 }[/math].
Graph Cohomology and Configuration Space Integrals (PDF)
Friday: Gauge invariance, Chern-Simons, holonomies.
Mar 9 is the last day to drop this class.
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| 9
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Mar 10
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Homework Assignment 7 (PDF)
Monday: The [math]\displaystyle{ gl(N) }[/math] weight system.
Wednesday: The universal property, hidden faces.
Friday: Insolubility of the quintic, naive expectations for CS perturbation theory.
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| 10
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Mar 17
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Homework Assignment 8 (PDF)
Monday: [math]\displaystyle{ W_{\mathfrak g}\colon{\mathcal A}(\uparrow)\to{\mathcal U}({\mathfrak g}) }[/math] and PBW.
Wednesday: The anomaly.
Friday: Faddeev-Popov, part I.
Gaussian Integration, Determinants, Feynman Diagrams (PDF).
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| 11
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Mar 24
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Homework Assignment 9 (PDF)
Monday: [math]\displaystyle{ {\mathcal A} }[/math] is a bi-algebra.
Wednesday: Understanding and fixing the anomaly.
Friday: class cancelled.
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| 12
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Mar 31
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Monday, Wednesday: class cancelled.
Friday: A Monday class: back to expansions.
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| E
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Apr 7
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Monday: A Friday class on what we mostly didn't have time to do.
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Add your name / see who's in!
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| Dror's Notebook
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Algebraic Knot Theory
Department of Mathematics, University of Toronto, Spring 2014
Agenda. Three courses on just one theorem: With [math]\displaystyle{ \mathcal K }[/math] the set of knots and [math]\displaystyle{ \mathcal A }[/math] something naturally associated to knots and quite related to Lie algebras, there exists an expansion [math]\displaystyle{ Z\colon\mathcal K\to\mathcal A }[/math].
Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, 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).
