\( \def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}} \def\calA{{\mathcal A}} \def\calD{{\mathcal D}} \def\calT{{\mathcal T}} \def\Lim{{\operatorname{Lim}}} \) © | Dror Bar-Natan: Classes: 2021-22:

MAT1350F - Algebraic Knot Theory and Computation

Toronto, Fall 2021

$$ $Essentials $$


Course Calendar

# 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: