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'''Instructor:''' {{Home Link||Dror Bar-Natan}}, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: {{Office Hours}}. |
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'''Instructor:''' {{Home Link||Dror Bar-Natan}}, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: {{Office Hours}}. |
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'''Classes.''' Mondays and Wednesdays at 11:10-12:00 and Fridays at 10:10-11:00 at Bahen 6180. |
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'''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. |
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{{Pensieve link|Classes/14-1350-AKT/About.pdf|About This Class}} (PDF). |
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{{Pensieve link|Classes/14-1350-AKT/About.pdf|About This Class}} (PDF). |
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[[Image:AKT-14-Conference.jpg|310px|center]] |
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[[Image:AKT-14-Conference.jpg|400px|center]] |
Latest revision as of 22:15, 13 January 2014
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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 .
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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, , and .
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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 .
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 . 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 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: 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: 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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![AKT-14-ClassPhoto.jpg](/images/thumb/9/98/AKT-14-ClassPhoto.jpg/310px-AKT-14-ClassPhoto.jpg) 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
the set of knots and
something naturally associated to knots and quite related to Lie algebras, there exists an expansion
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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).