Difference between revisions of "07-1352/Suggested Topics for Student Lectures"

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* BF theories.
 
* BF theories.
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* Finite type invariants of other kinds of objects (Legendrian and transverse knots, planar curves, etc.).
 +
 +
* Gropes and grope cobordism.
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 +
* The Lie algebra <math>gl(1|1)</math> and the Alexander polynomial.
 +
 +
* Gauss diagram formulas.
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 +
* Claspers and clovers.
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 +
* The Kalfagianni - Lin papers on Seifert surfaces and Vassiliev invariants.
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 +
* Rozansky-Witten theory.
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 +
* A detailed study of <math>\mathcal A</math> following Kneissler.
 +
 +
* Rozansky's rationality (ex-)conjecture.
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 +
* "Detecting Knot Invertibility" following Kuperberg.
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 +
* Multiple <math>\zeta</math>-numbers and the Drinfel'd associator.
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 +
* "Uniqueness" of a well-behaved universal finite type invariant.
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 +
* Finite type invariants ''not'' coming from Lie algebras, following Vogel and Lieberum.
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* The group of knots modulo <math>n</math>-equivalence.
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 +
* Vogel's "universal Lie Algebra".
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* Anything else from {{Dror}}'s [http://www.math.toronto.edu/~drorbn/papers/EMP/ EMP paper].
  
 
* Anything else from [http://www.pdmi.ras.ru/~duzhin/VasBib/ VasBib].
 
* Anything else from [http://www.pdmi.ras.ru/~duzhin/VasBib/ VasBib].
  
 
* Anything else from anywhere else.
 
* Anything else from anywhere else.

Revision as of 14:34, 6 February 2007

In Preparation

The information below is preliminary and cannot be trusted! (v)

Students must choose their lecture topics in coordination with Dror, and the sooner this is done, the better.

  • More on Chern-Simons theory, Feynman diagrams and configuration space integrals.
  • More on the Milnor Moore Theorem.
  • Explicit computations for torus knots, Hopf chains, etc.
  • Homotopy invariants of links.
  • Vassiliev invariants for braids.
  • Goussarov's "interdependent modifications".
  • The Melvin-Morton-Rozansky (ex-)Conjecture.
  • Finite type invariants of 3-manifolds.
  • The LMO invariant and the Århus integral.
  • Hutchings' step by step integration.
  • The exceptional Lie algebras and finite type invariants.
  • More on the self-linking number.
  • BF theories.
  • Finite type invariants of other kinds of objects (Legendrian and transverse knots, planar curves, etc.).
  • Gropes and grope cobordism.
  • The Lie algebra gl(1|1) and the Alexander polynomial.
  • Gauss diagram formulas.
  • Claspers and clovers.
  • The Kalfagianni - Lin papers on Seifert surfaces and Vassiliev invariants.
  • Rozansky-Witten theory.
  • A detailed study of \mathcal A following Kneissler.
  • Rozansky's rationality (ex-)conjecture.
  • "Detecting Knot Invertibility" following Kuperberg.
  • Multiple \zeta-numbers and the Drinfel'd associator.
  • "Uniqueness" of a well-behaved universal finite type invariant.
  • Finite type invariants not coming from Lie algebras, following Vogel and Lieberum.
  • The group of knots modulo n-equivalence.
  • Vogel's "universal Lie Algebra".
  • Anything else from anywhere else.