AKT-14/Class Photo

Our class on January 24, 2014:

Class Photo: click to enlarge

DBN: Classes: 2013-14: AKT-14 / Navigation

#	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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