140404-102655: General facts about $gr$. @AKT14 @Blackboard Shots @Academic Pensieve @Dror Bar-Natan

AKT14-{	hide text
140407-105125:	The Friday-Wednesday relation.
140407-104608:	The full Chern-Simons path integrals with ghosts, and its perturbative expansion.
140407-102836:	Random formulas.
140407-101549:	Faddeev-Popov.
140404-110419:	Horizontal compositions, generating tangles.
140404-105953:	The case of tangles.
140404-104947:	General algebraic structures.
140404-103527:	$A$-expansions.
140404-102655:	General facts about $gr$.
140404-102635:	Notices and reminders about expansions.
140326-110047:	Pulling back commutes with pushing forward.
140326-105711:	The proof of $dZ_0=A\cdot dZ_0$.
140326-103805:	Understanding and cancelling the anomaly.
140326-102116:	Review of the anomaly 2-form.
140324-113339:	Exercises.
140324-110108:	${\mathcal A}$ is a bi-algebra (2).
140324-105310:	${\mathcal A}$ is a bi-algebra.
140324-104340:	Examples of bi-algebras.
140324-103310:	Co-algebras, bi-algebras.
140324-102709:	Reminders, algebras.
140321-110354:	$\det(Q+\epsilon P)$ (2).
140321-105354:	$\det(Q+\epsilon P)$.
140321-104306:	Faddeev-Popov in the case of rotations on ${\mathbb R}^2$.
140321-103733:	The Faddeev-Popov determinant formula.
140319-110415:	The anomaly (3).
140319-105818:	The anomaly (2).
140319-104246:	The anomaly.
140319-103040:	Vanishing of the non-anomalous hidden faces.
140317-105925:	Universal PBW.
140317-104923:	PBW.
140317-103729:	$W_{\mathfrak g}$.
140317-102557:	${\mathcal U}({\mathfrak g})$.
140314-110347:	Naive expectations for perturbation theory.
140314-110240:	Finally, the Chern-Simon path integral.
140314-103456:	Insolubility of the quintic.
140312-110420:	Cancellation of most hidden faces (2).
140312-105957:	Cancellation of most hidden faces.
140312-104503:	$Z_0$ is a UFTI (if invariant).
140312-103108:	Reminders, a better formula for $Z_0$.
140310-100021:	A preview of bi-algebras.
140310-095320:	$4T$ for $gl(N)$.
140310-094743:	The $so(N)$ case.
140310-094353:	Further $gl(N)$ computations.
140310-093925:	A $gl(N)$ computation.
140310-092839:	The $gl(N)$ structure constants.
140310-091619:	Reminders.
140307-110330:	An iterated integral formula for the holonomy.
140307-105409:	The Chern-Simons form, holonomies.
140307-104129:	Motivation from physics, economics, and mathematics.
140307-101950:	Some formulas for gauge transformations.
140305-111609:	Chern-Simons and curvatures.
140305-110203:	${\mathcal A}$ arises!
140305-110128:	The adjoint of the graph differential (3).
140305-105737:	The adjoint of the graph differential (2).
140305-105506:	The adjoint of the graph differential.
140305-105317:	$Z_0$.
140305-103551:	Handout support.
140303-110402:	Not all invariant tensors arise this way.
140303-110019:	$W_{{\mathfrak g},R}$ satisfies IHX, AS, STU.
140303-104444:	Well-definededness of $W_{{\mathfrak g},R}$ (2).
140303-103342:	Well-definededness of $W_{{\mathfrak g},R}$.
140303-102902:	Informal `universallity' of the construction.
140303-102801:	The construction of $W_{{\mathfrak g},R}$.
140303-101621:	Reminders: the structure constants.
140228-105841:	Very naive gauge theory (2).
140228-105256:	Very naive gauge theory.
140228-104034:	Some diagrams.
140226-110208:	Graph cohomology and $\Omega_{dR}^\ast(\Gamma)$ (3).
140226-104550:	Graph cohomology and $\Omega_{dR}^\ast(\Gamma)$ (2).
140226-103415:	Graph cohomology and $\Omega_{dR}^\ast(\Gamma)$.
140224-110146:	The structure constants.
140224-105632:	Metrized Lie algebras.
140224-104701:	Constructing weight systems from Lie algebras.
140224-103753:	Lie algebras and representations.
140224-102332:	Reminders.
140214-110030:	Perturbed Gaussian integration and Feynman diagrams (2).
140214-105240:	Perturbed Gaussian integration and Feynman diagrams.
140214-103957:	Inverting the Laplacian.
140214-103102:	$L^-$ and $\Delta$.
140214-102429:	The $\delta$-function as an integral.
140214-101840:	Notes and plans, our section.
140212-110205:	The case of a knot in ${\mathbb R}^3$.
140212-105540:	Dealing with infra-red.
140212-103645:	Review of Fulton-MacPherson and the basic properties.
140210-110136:	${\mathcal A}(\bigcirc)\simeq{\mathcal A}(\uparrow)$.
140210-105758:	Proof of the invariance principle.
140210-105231:	The invariance principle.
140210-104841:	Proof of bracket-rise (2).
140210-104537:	Proof of bracket-rise.
140210-102624:	A table of dimensions, statement of bracket-rise.
140207-181713:	Homework Assignment 5.
140207-110017:	Gauge fixing and Hodge theory.
140207-105119:	The formula for $d^{-1}$.
140207-104454:	Stokes for pushforwards.
140207-104103:	Reminders on pushforwards.
140205-110540:	Manifolds with corners.
140205-104349:	Implementation.
140205-103009:	Clustering.
140203-111929:	The Fundamental Theorem is equivalent to a UFTI (2).
140203-105428:	The Fundamental Theorem is equivalent to a UFTI.
140203-104540:	The fundamental theorem, universal finite type invariants.
140203-103129:	The 4T relation and $\mathcal A$-spaces.
140203-102113:	Notes and reminders.
140131-183811:	Homework Assignment 4, Questions 1-2-3.
140131-110316:	Pushforwards.
140131-105659:	An integral formula for $d^{-1}$.
140131-104019:	$d^{-1}$ and linking numbers as intersection numbers.
140131-102906:	Reminders, 1-forms, 2-forms, cycles.
140129-110420:	Sign issues.
140129-105603:	A blatantly false theorem.
140129-105306:	The configuration space $C_D({\mathbb R}^3,\gamma)$.
140129-103734:	Swaddling maps and framings.
140129-102632:	Goals, a new formula for $sl_2$.
140127-110314:	The 4T relation.
140127-105732:	The FI relation.
140127-105435:	Weight systems and finiteness.
140127-104216:	$n$-singular knots and $n$-chord diagrams.
140127-103346:	The $n$th derivative is constant.
140127-102321:	HOMFLY-PT and Conway.
140127-101400:	Notes and reminders.
140124-190950:	Homework Assignment 3, Question 3.
140124-190949:	Homework Assignment 3, Questions 1 and 2.
140124-105724:	The second moments (2).
140124-104736:	The second moments.
140124-103755:	Moments of Gaussian integrals.
140124-102426:	Gaussian integration of arbitrary quadratics.
140124-101522:	Notices and today's goal.
140122-110556:	Little on Frenet-Serret.
140122-105652:	Framings and SO(3).
140122-104159:	Framings.
140122-102833:	Reminders.
140120-110110:	Jones is a FT series, proof.
140120-105912:	The Jones skein relation.
140120-103943:	Jones is a FT series.
140120-103110:	The definition of finite-type.
140120-102454:	$n$-singular knots and differentiating invariants.
140120-101022:	Notices and the proper spelling on Wensday.
140120-100933:	Reminder on Kauffman and Jones.
140117-185407:	Just a riddle, not a HW problem.
140117-185406:	Homework Assignment 2, Questions 2-3.
140117-185405:	Homework Assignment 2, Question 1.
140117-110102:	Volumes of spheres.
140117-104951:	The most-basic Gaussian integration.
140117-103851:	Minimization problems.
140117-102828:	The goal for 2-3 Fridays.
140115-110235:	Properties of $sl_1$.
140115-105829:	Swaddling.
140115-104033:	The naive self-linking integral.
140115-102559:	Reminders and degrees.
140113-110000:	The definition of the Jones polynomial.
140113-104126:	Ikke-invariance under R1 and the writhe.
140113-103403:	Invariance under R2 and R3.
140113-103143:	Computation for the trefoil.
140113-103130:	Definition of the Kauffman bracket.
140113-100835:	Notifications.
140110-192042:	Homework 1 (3).
140110-192041:	Homework 1 (2).
140110-191441:	Homework 1.
140110-105842:	Pythagoras' theorem.
140110-104943:	Recovering classical mechanics.
140110-102352:	Trotter's formula.
140110-102238:	Arriving at Schroedinger.
140108-120508:	An ugly explicit formula for the linking number integral.
140108-115840:	Alternative choice of volume forms.
140108-115225:	Invariance of the linking number integral.
140108-115001:	Computing the linking number integral.
140108-113910:	The linking number as an integral.
140108-113457:	Invariance of the linking number sum.
140108-112656:	The linking number as a sum over xings.
140108-111537:	Scheduling.
140106-120556:	Invariance of 3-colourings under Reidemeister moves.
140106-120118:	Reidemeister theorem and 3-colourings.
140106-114501:	Defining knots.
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