AKT-17

DBN: Classes: 2016-17: AKT-17 / Navigation

#	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 ${\mathfrak {g}}_{0}$ 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 ${\mathfrak {g}}_{0}$ 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: $\Gamma$ -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part I. Tuesday Hour 2: $\Gamma$ -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part II. Friday: The main ${\mathfrak {g}}_{0}$ 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 ${\mathfrak {g}}_{0}$ 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 ${\mathcal {K}}^{u}$ . Tuesday Hour 2: Algebraic structures on ${\mathcal {A}}^{u}$ . Friday: Conclusion of the ${\mathfrak {g}}_{0}$ discussion following 170303-g0LemmaAndInvariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
8	Mar 6	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). Tuesday Hour 2: The logos for ${\mathfrak {g}}_{1}$ following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb). Friday: Algebraic structures on ${\mathcal {A}}^{u}$ , 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 ${\mathfrak {g}}_{1}$ 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. 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 $sl_{3}$ , 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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