Difference between revisions of "07-1352/Suggested Topics for Student Lectures"
From Drorbn
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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.). | ||
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+ | * 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 [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
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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.
- 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 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 VasBib.
- Anything else from anywhere else.