07-1352/Class Notes for February 27 - Revision history

Drorbn at 01:37, 28 February 2007

2007-02-28T01:37:50Z

← Older revision		Revision as of 21:37, 27 February 2007
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	* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.		* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.
	* On to the Drinfel'd theory of associators. (Also see the [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/1_3Parenthesized_tangles.html section on parenthesized tangles] with the aborted [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/AlgebraicStructures.html Algebraic Structures on Knotted Objects and Universal Finite Type Invariants]).		* On to the Drinfel'd theory of associators. (Also see the [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/1_3Parenthesized_tangles.html section on parenthesized tangles] with the aborted [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/AlgebraicStructures.html Algebraic Structures on Knotted Objects and Universal Finite Type Invariants]).

			==Today's Lesson==

			Following today's class I ({{Dror}}) have started writing the paperlet [[The Kontsevich Integral for Knotted Trivalent Graphs]].

	==The Schematics of the Kontsevich Integral==		==The Schematics of the Kontsevich Integral==

Drorbn at 21:08, 27 February 2007

2007-02-27T21:08:31Z

← Older revision		Revision as of 17:08, 27 February 2007
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	* Today's material is '''separately''' simple and '''deep''', therefore {{Dror}} will get the chance to butcher it twice.		* Today's material is '''separately''' simple and '''deep''', therefore {{Dror}} will get the chance to butcher it twice.
			* Winding trails in uncharted territories, the problem with black boxes and teleportation, and the pathetic nature of mathematical research.
	* Recall the schematics of the Kontsevich Integral.		* Recall the schematics of the Kontsevich Integral.
	* Recall the fundamental theorem of finite type invariants for knotted trivalent graphs.		* Recall the fundamental theorem of finite type invariants for knotted trivalent graphs.

Drorbn at 21:02, 27 February 2007

2007-02-27T21:02:59Z

← Older revision		Revision as of 17:02, 27 February 2007
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	{{07-1352/Navigation}}		{{07-1352/Navigation}}
	{{In Preparation}}

	==Today's Agenda==		==Today's Agenda==

Drorbn at 21:02, 27 February 2007

2007-02-27T21:02:40Z

← Older revision		Revision as of 17:02, 27 February 2007
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	* The underlying ''basic truth'', assuming a "naive" Kontsevich integral for framed trivalent graphs exists.		* The underlying ''basic truth'', assuming a "naive" Kontsevich integral for framed trivalent graphs exists.
	* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.		* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.
			* On to the Drinfel'd theory of associators. (Also see the [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/1_3Parenthesized_tangles.html section on parenthesized tangles] with the aborted [http://www.math.toronto.edu/~drorbn/papers/AlgebraicStructures/AlgebraicStructures.html Algebraic Structures on Knotted Objects and Universal Finite Type Invariants]).
	* On to the Drinfel'd theory of associators.

	==The Schematics of the Kontsevich Integral==		==The Schematics of the Kontsevich Integral==

Drorbn at 20:44, 27 February 2007

2007-02-27T20:44:27Z

← Older revision		Revision as of 16:44, 27 February 2007
Line 9:		Line 9:
	* The underlying ''basic truth'', assuming a "naive" Kontsevich integral for framed trivalent graphs exists.		* The underlying ''basic truth'', assuming a "naive" Kontsevich integral for framed trivalent graphs exists.
	* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.		* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.
			* On to the Drinfel'd theory of associators.

	==The Schematics of the Kontsevich Integral==		==The Schematics of the Kontsevich Integral==

Drorbn at 20:42, 27 February 2007

2007-02-27T20:42:40Z

← Older revision		Revision as of 16:42, 27 February 2007
Line 1:		Line 1:
	{{07-1352/Navigation}}		{{07-1352/Navigation}}
	{{In Preparation}}		{{In Preparation}}

			==Today's Agenda==

			* Today's material is '''separately''' simple and '''deep''', therefore {{Dror}} will get the chance to butcher it twice.
			* Recall the schematics of the Kontsevich Integral.
			* Recall the fundamental theorem of finite type invariants for knotted trivalent graphs.
			* The underlying ''basic truth'', assuming a "naive" Kontsevich integral for framed trivalent graphs exists.
			* A sophisticated construction of the "naive" object, using ideas from renormalization theory and the renormalization group.

	==The Schematics of the Kontsevich Integral==		==The Schematics of the Kontsevich Integral==
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	{{07-1352/Schematics of the Kontsevich Integral}}		{{07-1352/Schematics of the Kontsevich Integral}}

	==The Fundamental Theorem of Finite Type Invariants==		==The Fundamental Theorem of Finite Type Invariants for Knotted Trivalent Graphs==

	{{06-1350/The Fundamental Theorem}}		{{06-1350/The Fundamental Theorem}}

Drorbn at 20:35, 27 February 2007

2007-02-27T20:35:58Z

New page

{{07-1352/Navigation}}
{{In Preparation}}

==The Schematics of the Kontsevich Integral==

{{07-1352/Schematics of the Kontsevich Integral}}

==The Fundamental Theorem of Finite Type Invariants==

{{06-1350/The Fundamental Theorem}}

==References==

{{note|MO}} J. Murakami and T. Ohtsuki, ''Topological Quantum Field Theory for the Universal Quantum Invariant'', Communications in Mathematical Physics '''188''' (1997) 501-520.