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| ===Department of Mathematics, University of Toronto, Spring 2017=== | | ===Department of Mathematics, University of Toronto, Spring 2017=== |
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− | '''Agenda.''' Group-discover and group-implement the strongest-ever truly-computable knot invariant; along the way, learn some of the why (topology!), what (Lie theory!), and how (Mathematica!). Leave behind a complete documentation trail. | + | '''Agenda.''' Group-discover and group-implement the strongest ever truly computable knot invariant; along the way, learn some of the why (topology!), what (Lie theory!), and how (Mathematica!). Leave behind a complete documentation trail. |
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| + | Alternatively, "understand everything in <span class=plainlinks>http://drorbn.net/GWU-1612/</span>, and beat it". |
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| '''Instructor:''' {{Home Link||Dror Bar-Natan}}, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: {{Office Hours}}. | | '''Instructor:''' {{Home Link||Dror Bar-Natan}}, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: {{Office Hours}}. |
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| '''Classes.''' Tuesdays 11-1 and Fridays 11-12 at Bahen 6180. Also a "HW meeting", covering no new material, on Fridays at 6:10PM at or near my office. | | '''Classes.''' Tuesdays 11-1 and Fridays 11-12 at Bahen 6180. Also a "HW meeting", covering no new material, on Fridays at 6:10PM at or near my office. |
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− | {{Pensieve link|Classes/17-1350-AKT/About.pdf|About This Class}} (PDF). | + | '''About This Class''' ({{Pensieve link|Classes/17-1350-AKT/About.pdf|pdf}}, {{Pensieve link|Classes/17-1350-AKT/About.html|html}}). |
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Latest revision as of 11:50, 30 December 2016
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Week of...
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Notes and Links
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1
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Jan 9
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Tuesday Hour 1: Course introduction as in About This Class (pdf, html). Tuesday Hour 2: The Jones polynomial via the Kauffman bracket, following 170110-JonesPoly.nb (pre-class: pdf, nb; post-class: pdf, nb). Friday: Knots, algebras, Yang-Baxter, CYBE, Lie algebras, universal enveloping algebras, formulas.
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2
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Jan 16
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Tuesday Hour 1: More on the Jones polynomial via the Kauffman bracket, following 170117-MoreJones.nb (pre-class: pdf, nb; post-class: pdf, nb). Tuesday Hour 2: Continuation, 170117-FastSlowRace.nb (pre-class: pdf, nb; post-class: pdf, nb), knot genus. Friday: The Lie algebra following 170120-g0.nb (pre-class: pdf, nb; post-class: pdf, nb).
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3
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Jan 23
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Tuesday Hour 1: Tangles and meta-monoids. Tuesday Hour 2: The fundamental group, meta-Hopf algebras, algebraic knot theory. Friday: The Lie algebra following 170127-g0.nb (pre-class: pdf, nb; post-class: pdf, nb). Class Photo.
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4
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Jan 30
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Tuesday Hour 1: Tangles, links, and 3-manifolds. Tuesday Hour 2: Genus, ribbon, slice. Friday: Normal orderings following 170203-g0dsO.nb (pre-class: pdf, nb; post-class: pdf, nb).
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5
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Feb 6
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Tuesday Hour 1: -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part I. Tuesday Hour 2: -calculus following 170207-GammaCalculus.nb (pre-class: pdf, nb; post-class: pdf, nb), part II. Friday: The main theorem following 170210-g0MainTheorem.nb (pre-class: pdf, nb; post-class: pdf, nb).
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6
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Feb 13
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Tuesday Hour 1: Expansions in general; also using 170214-ProgressiveScanning.nb (pre-class: pdf, nb; post-class: pdf, nb). Tuesday Hour 2: Expansions for tangles, finite type invariants. Friday: Computing the invariant following 170217-g0Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
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R
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Feb 20
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Reading Week.
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7
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Feb 27
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Tuesday Hour 1: Expansions and the fundamental theorem for . Tuesday Hour 2: Algebraic structures on . Friday: Conclusion of the discussion following 170303-g0LemmaAndInvariant.nb (pre-class: pdf, nb; post-class: pdf, nb).
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8
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Mar 6
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Tuesday Hour 1: The polished invariant following 170307-g0Polished.nb (pre-class: pdf, nb; post-class: pdf, nb) and lemmas following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb). Tuesday Hour 2: The logos for following 170307-geps.nb (pre-class: pdf, nb; post-class: pdf, nb). Friday: Algebraic structures on , trivalent diagrams.
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9
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Mar 13
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Monday is the last day to drop this class. Friday: Deriving and testing the Logos following 170317-g1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170317-TestingTheLogos.nb (pre-class: pdf, nb; post-class: pdf, nb).
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10
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Mar 20
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Tuesday Hour 1: The invariant following 170321-g1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170321-Polishedg1Invariant.nb (pre-class: pdf, nb; post-class: pdf, nb). Tuesday Hour 2: offline, though see BBS/AKT17-170321-145350.jpg and BBS/AKT17-170321-150540.jpg. Friday: Associators, also following 170324-Associator.nb (pre-class: pdf, nb; post-class: pdf, nb) and 170324-MutipleZetaValues.pdf.
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11
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Mar 27
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Classes canceled due to an MSRI workshop.
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12
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Apr 3
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Tuesday Hour 1: Diagrams to Universal Enveloping Algebras, the u-case. Tuesday Hour 2: Virtual knots and diagrams to Universal Enveloping Algebras, the v-case. Friday: Sjabbo Schaveling: The Quantum Double towards , following 170407-Classical_Algebra_E0.nb (pdf, nb), 170407--Quantum_Algebra_E0.nb (pdf, nb), and 170407--E_machten_Algebra_E0_v2.nb (pdf, nb).
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Add your name / see who's in!
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Dror's Notebook
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Algebraic Knot Theory - Poly-Time Computations
Department of Mathematics, University of Toronto, Spring 2017
Agenda. Group-discover and group-implement the strongest ever truly computable knot invariant; along the way, learn some of the why (topology!), what (Lie theory!), and how (Mathematica!). Leave behind a complete documentation trail.
Alternatively, "understand everything in http://drorbn.net/GWU-1612/, and beat it".
Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.
Classes. Tuesdays 11-1 and Fridays 11-12 at Bahen 6180. Also a "HW meeting", covering no new material, on Fridays at 6:10PM at or near my office.
About This Class (pdf, html).