| # | Week of ... | |
| 1 | September 7 |
UofT graduate classes begin on Tuesday September 8 and our first class is on
Wednesday September 9.
Handout: $$make_page {name => 'About', title => 'About This Class'}$$. Wednesday: Knots, knot diagrams, Reidemeister moves, 3-colourings. Videos: @dbnvp, @YouTube. Friday: The Kauffman Bracket. Videos: @dbnvp, @YouTube. Class notes for week 1. |
| 2 | September 14 |
Monday: The Jones polynomial and implementation. Videos: @dbnvp, @YouTube.
Mathematica session: pdf,
nb.
Wednesday: Faster implementations of the bracket. Videos: @dbnvp, @YouTube. Mathematica session: pdf, nb. $$make_page {name => 'HW1', title => 'Homework Assignment 1'}$$. Friday: Tangles and planar algebras. Videos: @dbnvp, @YouTube. Class notes for week 2. |
| 3 | September 21 | Monday: Last day to add this class.
Monday: End of the Jones story, beginning of Khovanov's. Videos: @dbnvp, @YouTube. $$make_page {name => 'HW2', title => 'Homework Assignment 2'}$$. Wednesday: Complexes, heights, degrees. Videos: @dbnvp, @YouTube. Wednesday: HW1 was due at 11:59PM. Friday: Constructing the Khovanov complex. Videos: @dbnvp, @YouTube. Class notes for week 3. |
| 4 | September 28 |
Monday: Products, co-products, the Frobenius condition. Videos: @dbnvp, @YouTube.
$$make_page {name => 'HW3', title => 'Homework Assignment 3'}$$. Wednesday: Proof of invariance of Khovanov homology. Videos: @dbnvp, @YouTube. Wednesday: HW2 due at 11:59PM. Friday: Some computations of Khovanov homology; finite type invariants. Videos: @dbnvp, @YouTube. Class notes for week 4. |
| 5 | October 5 |
Monday: Examples of finite-type invariants. Videos: @dbnvp, @YouTube.
Wednesday: Chord diagrams, weight systems, FI, 4T. Videos: @dbnvp, @YouTube. $$make_page {name => 'HW4', title => 'Homework Assignment 4'}$$. Wednesday: HW3 due at 11:59PM. Friday: The Algebra ${\mathcal A}$. Videos: @dbnvp, @YouTube. Class notes for week 5. |
| 6 | October 12 |
Monday is Thanksgiving; no class.
Wednesday: $W_C$ and $\Box$. Videos: @dbnvp, @YouTube. Current class notes. $$make_page {name => 'HW5', title => 'Homework Assignment 5'}$$. Thursday: HW4 due at 11:59PM. Friday: $\calA$ and $\calA^t$. Videos: @dbnvp, @YouTube. Class notes for week 6. |
| 7 | October 19 |
Monday: $\calA$ and $\calA^t$, Lie algebras. Videos: @dbnvp, @YouTube.
Wednesday: Lie algebraic weight systems. Videos: @dbnvp, @YouTube. $$make_page {name => 'HW6', title => 'Homework Assignment 6'}$$. Wednesday: HW5 was due at 11:59PM. Friday: $gl(N)$ and $sl(2)$. Videos: @dbnvp, @YouTube. Class notes for week 7. |
| 8 | October 26 |
Monday: The Four Colour Theorem, Universal Finite Type Invariants. Videos: @dbnvp, @YouTube.
Monday: Last day to drop this class. Wednesday: On HW6, on cosmic coincidences. Videos: @dbnvp, @YouTube. Friday: Cosmic coincidences and IHX. Videos: @dbnvp, @YouTube. Class notes for week 8. Friday: HW6 is due at 11:59PM. |
| 9 | November 2 |
Monday: A quick and vague introduction to Feynman diagrams. Videos: @dbnvp, @YouTube.
Wednesday: The Knot Group. Videos: @dbnvp, @YouTube. $$make_page {name => 'HW7', title => 'Homework Assignment 7'}$$. Friday: The power of the Knot Group. Videos: @dbnvp, @YouTube. Class notes for week 9. |
| R | November 9 | Undergraduate Reading Week - no classes. |
| 10 | November 16 |
Monday: Knot colourings and quandles. Videos: @dbnvp, @YouTube.
Wednesday: Mostly computer trouble, plus little more about quandles and little about Seifert surfaces. Videos: @dbnvp, @YouTube. Wednesday: HW7 due. $$make_page {name => 'HW8', title => 'Homework Assignment 8'}$$. Friday: Seifert surfaces and the genus. Videos: @dbnvp, @YouTube. Class notes for week 10. |
| 11 | November 23 |
Monday: Proof of the additivity of the genus. Videos: @dbnvp, @YouTube.
Wednesday: Continuous pathologies in R^3, and some smooth theorems. Videos: @dbnvp, @YouTube. Thursday: HW9 is on Crowdmark and here. Thursday: HW8 due. Friday: Proof of unique factorization. Videos: @dbnvp, @YouTube. Class notes for week 11. |
| 12 | November 30 |
Monday: Braids, closures, and links. Videos: @dbnvp, @YouTube.
Wednesday: Braids and complexity, pure braids, semi-direct products. Videos: @dbnvp, @YouTube. Thursday: HW10 is on Crowdmark and here. Thursday: HW9 was due. Friday: Combing braids. PvB and PwB. Videos: @dbnvp, @YouTube. Class notes for week 12. |
| 13 | December 7 |
Monday: More on w-braids and v-knots. Videos: @dbnvp, @YouTube.
Lickorish on unique factorization. Wednesday: Expansions for groups. Videos: @dbnvp, @YouTube. Class notes for week 13. Wednesday: HW10 due at 11:59PM. |
Further resources:
