AKT-17/Navigation
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# | Week of... | Notes and Links |
---|---|---|
1 | Jan 9 | 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. |
2 | Jan 16 | 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 following 170120-g0.nb (pre-class: pdf, nb; post-class: pdf, nb). |
3 | Jan 23 | Tuesday Hour 1: Tangles and meta-monoids. Tuesday Hour 2: The fundamental group, meta-Hopf algebras, algebraic knot theory. Friday: The Lie algebra following 170127-g0.nb (pre-class: pdf, nb; post-class: pdf, nb). Class Photo. |
4 | Jan 30 | 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). |
5 | Feb 6 | Tuesday Hour 1: -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part I. Tuesday Hour 2: -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part II. Friday: The main theorem following 170210-g0MainTheorem.nb (pre-class: pdf, nb; post-class: pdf, nb). |
6 | Feb 13 | 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 invariant following 170217-g0Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb). |
R | Feb 20 | Reading Week. |
7 | Feb 27 | Tuesday Hour 1: Expansions and the fundamental theorem for . Tuesday Hour 2: Algebraic structures on . Friday: Conclusion of the discussion following 170303-g0LemmaAndInvariant.nb (pre-class: pdf, nb; post-class: pdf, nb). |
8 | Mar 6 | Tuesday Hour 1: The polished invariant following 170307-g0Polished.nb (pre-class: pdf, nb; post-class: pdf, nb) and lemmas following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb). Tuesday Hour 2: The logos for following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb). Friday: Algebraic structures on , trivalent diagrams. |
9 | Mar 13 | 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). |
10 | Mar 20 | Tuesday Hour 1: The 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. |
11 | Mar 27 | Classes canceled due to an MSRI workshop. |
12 | Apr 3 | 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 , 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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