View source for 07-1352/Suggested Topics for Student Lectures

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{|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.