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). Add your name / see who's in! Dror's Notebook

Algebraic Knot Theory - Poly-Time Computations

Department of Mathematics, University of Toronto, Spring 2017

Agenda. Group-discover-and-implement the strongest-ever truly-computable knot invariant; along the way, learn some of the why (topology!), what (Lie theory!), and how (Mathematica!). Leave behind a complete documentation trail.

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes. Tuesdays 11-1 and Fridays 11-12 at Bahen 6180.

About This Class (PDF).