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**Notes on AKT-140314:**
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Insolubility of the quintic, naive expectations for CS perturbation theory.

# | Week of... | Notes and Links |
---|---|---|

1 | Jan 6 | About This Class (PDF). Monday: Course introduction, knots and Reidemeister moves, knot colourings. Tricolourability without Diagrams Wednesday: The Gauss linking number combinatorially and as an integral. Friday: The Schroedinger equation and path integrals. Friday Introduction (the quantum pendulum) |

2 | Jan 13 | Homework Assignment 1. Monday: The Kauffman bracket and the Jones polynomial. Wednesday: Self-linking using swaddling. Friday: Euler-Lagrange problems, Gaussian integration, volumes of spheres. |

3 | Jan 20 | Homework Assignment 2. Monday: The definition of finite-type and some examples. Wednesday: The self-linking number and framings. Friday: Integrating a polynomial times a Gaussian. Class Photo. |

4 | Jan 27 | Homework Assignment 3. Monday: Chord diagrams and weight systems. Wednesday: Swaddling maps and framings, general configuration space integrals. Friday: Some analysis of . |

5 | Feb 3 | Homework Assignment 4. Monday: 4T, the Fundamental Theorem and universal finite type invariants. The Fulton-MacPherson Compactification (PDF). Wednesday: The Fulton-MacPherson Compactification, Part I. Friday: More on pushforwards, , and . |

6 | Feb 10 | Homework Assignment 5. Monday: The bracket-rise theorem and the invariance principle. Wednesday: The Fulton-MacPherson Compactification, Part II. Friday: Gauge fixing, the beginning of Feynman diagrams. |

R | Feb 17 | Reading Week. |

7 | Feb 24 | Monday: A review of Lie algebras. Wednesday: Graph cohomology and . Friday: More on Feynman diagrams, beginning of gauge theory. From Gaussian Integration to Feynman Diagrams (PDF). |

8 | Mar 3 | Homework Assignment 6 (PDF) Monday: Lie algebraic weight systems. Wednesday: Graph cohomology and the construction of . Graph Cohomology and Configuration Space Integrals (PDF) Friday: Gauge invariance, Chern-Simons, holonomies. Mar 9 is the last day to drop this class. |

9 | Mar 10 | Homework Assignment 7 (PDF) Monday: The weight system. Wednesday: The universal property, hidden faces. Friday: Insolubility of the quintic, naive expectations for CS perturbation theory. |

10 | Mar 17 | Homework Assignment 8 (PDF) Monday: and PBW. Wednesday: The anomaly. Friday: Faddeev-Popov, part I. Gaussian Integration, Determinants, Feynman Diagrams (PDF). |

11 | Mar 24 | Homework Assignment 9 (PDF) Monday: is a bi-algebra. Wednesday: Understanding and fixing the anomaly. Friday: class cancelled. |

12 | Mar 31 | Monday, Wednesday: class cancelled. Friday: A Monday class: back to expansions. |

E | Apr 7 | Monday: A Friday class on what we mostly didn't have time to do. |

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panel Managed by dbnvp: Tip: blackboard shots are taken when the discussion of their content has just ended. To see the beginning of the discussion on a certain blackboard, roll the video to the time of the preceeding blackboard.

panel Managed by dbnvp: Tip: blackboard shots are taken when the discussion of their content has just ended. To see the beginning of the discussion on a certain blackboard, roll the video to the time of the preceeding blackboard.

- I have one comment- you claim it is weaker than Galois. At least in one important aspect I think it is much stronger. I challenge you to show with Galois theory that if we add exp(z) to our list of allowed operations, a solution cannot be found...
- In fact, I guess you can add to the list of allowed functions any continuous multivalued function with up to 4 values and it won't help (of course with 5 values you can solve it since the solution is such a function...). Am I right?

I believe Boaz is right, and he is making a very strong point - not only there is no formula for the roots of a quadratic in terms of radicals - in fact this remains true even if we are allowed to use other *univalent* functions (or even up to 4-valent).