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AKT-140314 Video

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Videography by Iva Halacheva troubleshooting

Notes on AKT-140314: [edit, refresh]

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 $d^{-1}$ .
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, $d^{-1}$ , and $d^\ast$ .
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 $\Omega_{dR}^\ast(\Gamma)$ . 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 $Z_0$ . 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 $gl(N)$ 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: $W_{\mathfrak g}\colon{\mathcal A}(\uparrow)\to{\mathcal U}({\mathfrak g})$ and PBW. Wednesday: The anomaly. Friday: Faddeev-Popov, part I. Gaussian Integration, Determinants, Feynman Diagrams (PDF).
11	Mar 24	Homework Assignment 9 (PDF) Monday: ${\mathcal A}$ 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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Dror's Notebook

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0:00:00 [edit] The YouTube video by Boaz Katz is at http://youtu.be/RhpVSV6iCko.

0:02:29 [edit] Boaz wrote:

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).

0:06:13 [edit] Start of the quintic discussion.

0:22:56 [add] Insolubility of the quintic.

0:50:40 [add] Finally, the Chern-Simon path integral.

0:51:47 [add] Naive expectations for perturbation theory.

width: 400 720	download ogg/AKT-140314_400.ogg


Videography by Iva Halacheva	troubleshooting