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Week of...
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Notes and Links
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| 1
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Jan 9
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 Tuesday Hour 1: Course introduction as in About This Class (pdf, html).
Tuesday Hour 2: The Jones polynomial via the Kauffman bracket, following 170110-JonesPoly.nb (pre-class: pdf, nb; post-class: pdf, nb).
Friday: Knots, algebras, Yang-Baxter, CYBE, Lie algebras, universal enveloping algebras, formulas.
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| 2
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Jan 16
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Tuesday Hour 1: More on the Jones polynomial via the Kauffman bracket, following 170117-MoreJones.nb (pre-class: pdf, nb; post-class: pdf, nb).
Tuesday Hour 2: Continuation, 170117-FastSlowRace.nb (pre-class: pdf, nb; post-class: pdf, nb), knot genus.
Friday: The Lie algebra [math]\displaystyle{ {\mathfrak g}_0 }[/math] following 170120-g0.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| 3
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Jan 23
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Tuesday Hour 1: Tangles and meta-monoids.
Tuesday Hour 2: The fundamental group, meta-Hopf algebras, algebraic knot theory.
Friday: The Lie algebra [math]\displaystyle{ {\mathfrak g}_0 }[/math] following 170127-g0.nb (pre-class: pdf, nb; post-class: pdf, nb).
Class Photo.
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| 4
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Jan 30
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Tuesday Hour 1: Tangles, links, and 3-manifolds.
Tuesday Hour 2: Genus, ribbon, slice.
Friday: Normal orderings following 170203-g0dsO.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| 5
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Feb 6
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Tuesday Hour 1: [math]\displaystyle{ \Gamma }[/math]-calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part I.
Tuesday Hour 2: [math]\displaystyle{ \Gamma }[/math]-calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part II.
Friday: The main [math]\displaystyle{ {\mathfrak g}_0 }[/math] theorem following 170210-g0MainTheorem.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| 6
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Feb 13
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Tuesday Hour 1: Expansions in general; also using 170214-ProgressiveScanning.nb (pre-class: pdf, nb; post-class: pdf, nb).
Tuesday Hour 2: Expansions for tangles, finite type invariants.
Friday: Computing the [math]\displaystyle{ {\mathfrak g}_0 }[/math] invariant following 170217-g0Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| R
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Feb 20
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Reading Week.
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| 7
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Feb 27
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Tuesday Hour 1: Expansions and the fundamental theorem for [math]\displaystyle{ {\mathcal K}^u }[/math].
Tuesday Hour 2: Algebraic structures on [math]\displaystyle{ {\mathcal A}^u }[/math].
Friday: Conclusion of the [math]\displaystyle{ {\mathfrak g}_0 }[/math] discussion following 170303-g0LemmaAndInvariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| 8
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Mar 6
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Tuesday Hour 1: The polished [math]\displaystyle{ {\mathfrak g}_0 }[/math] invariant following 170307-g0Polished.nb (pre-class: pdf, nb; post-class: pdf, nb) and [math]\displaystyle{ {\mathfrak g}_1 }[/math] lemmas following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb).
Tuesday Hour 2: The logos for [math]\displaystyle{ {\mathfrak g}_1 }[/math] following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb).
Friday: Algebraic structures on [math]\displaystyle{ {\mathcal A}^u }[/math], trivalent diagrams.
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| 9
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Mar 13
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Monday is the last day to drop this class.
Friday: Deriving and testing the Logos following 170317-g1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170317-TestingTheLogos.nb (pre-class: pdf, nb; post-class: pdf, nb).
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| 10
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Mar 20
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Tuesday Hour 1: The [math]\displaystyle{ {\mathfrak g}_1 }[/math] invariant following 170321-g1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170321-Polishedg1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
Tuesday Hour 2: offline, though see BBS/AKT17-170321-145350.jpg and BBS/AKT17-170321-150540.jpg.
Friday: Associators, also following 170324-Associator.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170324-MutipleZetaValues.pdf.
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| 11
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Mar 27
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Classes canceled due to an MSRI workshop.
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| 12
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Apr 3
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Tuesday Hour 1: Diagrams to Universal Enveloping Algebras, the u-case.
Tuesday Hour 2: Virtual knots and diagrams to Universal Enveloping Algebras, the v-case.
Friday: Sjabbo Schaveling: The Quantum Double towards [math]\displaystyle{ sl_3 }[/math], following 170407-Classical_Algebra_E0.nb (pdf, nb), 170407--Quantum_Algebra_E0.nb (pdf, nb), and 170407--E_machten_Algebra_E0_v2.nb (pdf, nb).
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