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

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{{07-1352/Navigation}}
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{{In Preparation}}
{|align=center cellspacing=0 border=1 cellpadding=3
|- align=center
|colspan=2|'''The Choices'''
|- align=left
|Karene
| <math>gl(1|1)</math>
|- align=left
|Siddarth
| The Melvin-Morton-Rozansky (ex-)Conjecture.
|- align=left
|Zavosh
|Knot Floer homology
|- align=left
|Zsuzsi
|Vogel's universal algebra
|}

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.

* Higher skein modules following Andersen and Turaev, {{arXiv|math.GT/9812071}}.

* 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 &Aring;rhus 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 <math>gl(1|1)</math> 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 <math>\mathcal A</math> following Kneissler.

* Rozansky's rationality (ex-)conjecture.

* "Detecting Knot Invertibility" following Kuperberg.

* Multiple <math>\zeta</math>-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 <math>n</math>-equivalence.

* Vogel's "universal Lie Algebra".

* 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 anywhere else.

Latest revision as of 10:04, 20 March 2007

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2 Jan 16 Notes
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11 Mar 27 Notes
12 Apr 3 Map
13 Apr 10 Dancso
SP Apr 17 Chu, Sankaran, Amir-Khosravi
Suggested Student Topics
The Choices
Karene
Siddarth The Melvin-Morton-Rozansky (ex-)Conjecture.
Zavosh Knot Floer homology
Zsuzsi Vogel's universal algebra

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 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 following Kneissler.
  • Rozansky's rationality (ex-)conjecture.
  • "Detecting Knot Invertibility" following Kuperberg.
  • Multiple -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 -equivalence.
  • Vogel's "universal Lie Algebra".
  • Anything else from anywhere else.
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