AKT-17/Navigation

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Back to AKT-17.

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