AKT-14

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. Add your name / see who's in! Dror's Notebook

Algebraic Knot Theory

Department of Mathematics, University of Toronto, Spring 2014

Agenda. Three courses on just one theorem: With ${\mathcal {K}}$ the set of knots and ${\mathcal {A}}$ something naturally associated to knots and quite related to Lie algebras, there exists an expansion $Z\colon {\mathcal {K}}\to {\mathcal {A}}$.

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes. Mondays, Wednesdays, and Fridays at 10:10-11:00; Mondays and Fridays at Bahen 6180 but Wednesdays at Huron 1018. There will also be a "HW meeting", covering no new material, on Fridays at 6:10PM at Bahen 6180.

About This Class (PDF).