# Week of... Videos, Notes, and Links
: 3-colourings, Reidemeister's theorem, invariance, the Kauffman bracket.
: R23 invariance of the bracket, R1, the writhe, the Jones polynomial, programming the Jones polynomial.
Tricolourability
2 Sep 14 : More on Jones, some pathologies and more on Reidemeister, our overall agenda.
: The definition of finite type, weight systems, Jones is a finite type series.
: The skein relation for Jones; HOMFLY-PT and Conway; the weight system of Jones.
3 Sep 21 : FI, 4T, HOMFLY and FI and 4T, statement of the Fundamental Theorem, framed knots.
: Some dimensions of ${\displaystyle {\mathcal {A}}_{n}}$, ${\displaystyle {\mathcal {A}}}$ is a commutative algebra, ${\displaystyle {\mathcal {A}}(\bigcirc )\equiv {\mathcal {A}}(\uparrow )}$.
Class Photo
: ${\displaystyle {\mathcal {A}}}$ is a co-commutative algebra, the relation with products of invariants, ${\displaystyle {\mathcal {A}}}$ is a bi-algebra.
4 Sep 28 Homework Assignment 1
Homework Assignment 1 Solutions
: The Milnor-Moore theorem, primitives, the map ${\displaystyle {\mathcal {A}}^{r}\to {\mathcal {A}}}$.
: Jacobi diagrams, AS, IHX, STU, and the equivalence of all that with 4T.
: The very basics on Lie algebras.
5 Oct 5 : Lie algebraic weight systems, ${\displaystyle gl_{N}}$.
: More on ${\displaystyle gl_{N}}$, Lie algebras and the four colour theorem.
: The "abstract tenssor" approach to weight systems, ${\displaystyle {\mathcal {U}}({\mathfrak {g}})}$ and PBW, the map ${\displaystyle {\mathcal {T}}_{\mathfrak {g}}}$.
6 Oct 12 : Algebraic properties of ${\displaystyle {\mathcal {U}}({\mathfrak {g}})}$ vs. algebraic properties of ${\displaystyle {\mathcal {A}}}$.
Thursday's class canceled.
7 Oct 19 : Universal finite type invariants, filtered and graded spaces, expansions.
Homework Assignment 2
The Stonehenge Story
: The Stonehenge Story to IHX and STU.
: The Stonhenge Story: anomalies, framings, relation with physics.
8 Oct 26 : Knotted trivalent graphs and their chord diagrams.
: Zsuzsi Dancso on the Kontsevich Integral (1).
: Zsuzsi Dancso on the Kontsevich Integral (2).
9 Nov 2 : The details of ${\displaystyle {\mathcal {A}}^{TG}}$.
: Three basic problems: genus, unknotting numbers, ribbon knots.
: The three basic problems and algebraic knot theory.
10 Nov 9 : Tangles and planar algebras, shielding and the generators of KTG.
Homework Assignment 3
No Thursday class.
11 Nov 16 Local Khovanov Homology
: Local Khovanov homology, I.
: Local Khovanov homology, II.
12 Nov 23 : Emulation of one structure inside another, deriving the pentagon.
: Peter Lee on braided monoidal categories, I.
: Peter Lee on braided monoidal categories, II.
13 Nov 30 : The relations in KTG.
: The Existence of the Exponential Function.
: The Final Exam, Dror's failures.
F Dec 7 The Final Exam on Thu Dec 10, 9-11, Bahen 6183.
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