| # | Week of ... | |
| 1 | September 6 |
UofT graduate classes begin on Thursday September 9 and our first class is on
Friday September 10.
Handout: $$make_page {name => 'NonObvious', title => 'Some Non Obvious Examples'}$$. Handout: $$framed_page {name => 'Zoo', title => 'A Knot Zoo', url=> 'https://knotplot.com/zoo/', external => 1}$$. Handout: $$framed_page {name => 'Plan', title => 'Tentative Plan', url=> 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/Plan-210910.pdf', external => 0}$$. Handout: $$make_page {name => 'About', title => 'About This Class'}$$. Friday: Course Introduction. Videos: @dbnvp, @YouTube. |
| 2 | September 13 |
Monday: What are knots? And a word about the Kauffman bracket. Videos: @dbnvp, @YouTube.
Wednesday: The Jones polynomial and implementation. Videos: @dbnvp, @YouTube. Mathematica session: pdf, nb. $$make_page {name => 'HW01', title => 'Homework Assignment 1'}$$. Friday: A faster Jones program. Videos: @dbnvp, @YouTube. Mathematica session 1: pdf, nb. Mathematica session 2: pdf, nb. |
| 3 | September 20 |
Monday: Tangles and planar algebras. Videos: @dbnvp, @YouTube.
Link: $$framed_page {name => 'OnBeyondZebra', title => 'On Beyond Zebra!', url=> 'https://en.wikipedia.org/wiki/On_Beyond_Zebra!', external => 1}$$. Wednesday: Genus, the ribbon property. Videos: @dbnvp, @YouTube. Handout: $$framed_page {name => 'KnotsAndSurfaces', title => 'Knots and Surfaces', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/KnotsAndSurfaces.pdf'}$$. Friday: Surfaces and the Seifert algorithm. Videos: @dbnvp, @YouTube. $$framed_page {name => 'HW02', title => 'Homework Assignment 2', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/HW02.pdf'}$$. |
| 4 | September 27 |
Monday: Tangles, genus, ribbon. Videos: @dbnvp, @YouTube.
Wednesday: The Yang-Baxter technique. Videos: @dbnvp, @YouTube. Friday: IHOP Algebras, $R$-Elements, and $WG$. Videos: @dbnvp, @YouTube. Mathematica session: pdf, nb. Handout: $$framed_page {name => 'IHOP-R-WG', title => 'IHOP Algebras, $R$-Elements, and $WG$', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/IHOP-R-WG.pdf'}$$. $$framed_page {name => 'HW03', title => 'Homework Assignment 3', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/HW03.pdf'}$$. |
| 5 | October 4 |
Monday: Computations with WG. Videos: @dbnvp, @YouTube.
Mathematica session:
pdf,
nb.
Wednesday: Meta-monoids and virtual tangles. Videos: @dbnvp, @YouTube. Friday: Rotational Virtual Knots (1). Videos: @dbnvp, @YouTube. $$framed_page {name => 'HW04', title => 'Homework Assignment 4', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/HW04.pdf'}$$. |
| 6 | October 11 |
Monday is Thanksgiving; no class.
Wednesday: The Kerler Algebra. Videos: @dbnvp, @YouTube. Mathematica session: pdf, nb. Friday: The 4x4 Alexander R-Matrix; conversions to RVK. Videos: @dbnvp, @YouTube. Mathematica session: pdf, nb. |
| 7 | October 18 |
Monday: More computations, a bit on the Heisenberg algebra. Videos: @dbnvp, @YouTube.
Mathematica session: Common@.nb -
pdf,
nb
and 4DAlexander2@.nb -
pdf,
nb.
Wednesday: More on the Heisenberg algebra and a bit on generating functions. Videos: @dbnvp, @YouTube. Friday: The generating function of the Heisenberg multiplication. Videos: @dbnvp, @YouTube. |
| 8 | October 25 |
Monday: Composing generating functions. Videos: @dbnvp, @YouTube.
Wednesday: Composing Gaussians. Videos: @dbnvp, @YouTube. Mathematica session: GDO-Heisenberg@.pdf, GDO-Heisenberg@.nb. Friday: Implementing GDO. Videos: @dbnvp, @YouTube. Mathematica session: GDO-Heisenberg2@.pdf, GDO-Heisenberg2@.nb. |
| 9 | November 1 |
Monday: Contracting Gaussians: Algebra by the means of partial differential equations. Videos: @dbnvp, @YouTube.
Wednesday: Contracting Gaussians (2). Videos: @dbnvp, @YouTube. Friday: Gamma Calculus. Videos: @dbnvp, @YouTube. |
| R | November 8 | Reading Week, no classes. |
| 10 | November 15 |
Monday: Perturbed Gaussian Integration. Videos: @dbnvp, @YouTube.
Wednesday: Feynman Diagrams. Videos: @dbnvp, @YouTube. Friday: Philosophical review. Videos: @dbnvp, @YouTube. |
| 11 | November 22 |
Monday: Lemmas 1 and 2. Videos: @dbnvp, @YouTube.
Wednesday: Perturbations and PDEs. Videos: @dbnvp, @YouTube. Mathematica session: PerturbedHeisenberg.pdf, PerturbedHeisenberg.nb. Friday: Computations with perturbed Heisenberg. Videos: @dbnvp, @YouTube. Mathematica session: PerturbedHeisenberg2@.pdf, PerturbedHeisenberg2@.nb. |
| 12 | November 29 |
Monday: CU and QU. Videos: @dbnvp, @YouTube.
Handout: $$framed_page {name => 'CUQU', title => 'CU and QU', url=> 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/CUQU.pdf', external => 0}$$. $$framed_page {name => 'HW05', title => 'Homework Assignment 5', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/HW05.pdf'}$$. Wednesday: Multiplication in CU. Videos: @dbnvp, @YouTube. Friday: Mostly DPG2. Videos: @dbnvp, @YouTube. |
| 13 | December 6 |
Monday: Primitive and Group Like Elements. Videos: @dbnvp, @YouTube.
Wednesday: Discussion; not recorded. $$framed_page {name => 'HW06', title => 'Homework Assignment 6', external => 0, url => 'https://drorbn.net/AcademicPensieve/Classes/21-1350-KnotTheory/HW06.pdf'}$$. |
Further resources:
