Blackboard Shots with Prefix "AKT14"

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.