To get a grade in this class, write a nifty
report on one of the topics below. Your report **must** be
mathematically non-empty (reading it, the other students in this class
should learn something new from it, beyond notation). Also, elegance
counts! You should aim for presentation quality - I hope to
eventually post your projects on this site (with your permissions, of
course).

**Possible Topics:**

- Goussarov's alternative
definition of finite type invariants, as in his paper
*Interdependent modifications of links and invariants of finite degree*, Topology**37-3**(1998). - The relationship with the Chern-Simons quantum field theory, as for example in my thesis and in many later and better sources such as Dylan Thurston's thesis, arXiv:math.QA/9901110.
- The Le-Murakami notion of q-tangles (arXiv:hep-th/9401016) or the Bar-Natan notion of non associative tangles (here; yikes, how much I regret this name. "Paranthesized tangles" is much better).
- Write an elegant (and correct) exposition of how operations on knotted objects and invariants of knotted objects induce operations on chord diagrams (multiplying invariants, doubling a component, etc.). This, at least partially, was done by Willerton.
- Something on Kontsevich's original proof of the existence of a
universal finite type invariant. See e.g. my paper
*On the Vassiliev Knot Invariants*, or the paper*The Kontsevich Integral*by Chmutov and Duzhin. - Something on Hutchings' approach to
the proof of the fundamental theorem, which is successful in the case
of braids but still open in the case of knots. See his paper
*Integration of Singular Braid Invariants and Graph Cohomology*or my review of it (with Stoimenow)*The Fundamental Theorem of Vassiliev Invariants*or my unfinished exposition*Finite Type Invariants by the Species*. - Anything else. You may find some ideas here or just drop by and talk to me.

Background image: A table of knots and links by Rob Scharein, taken from http://www.cs.ubc.ca/nest/imager/contributions/scharein/zoo/knotzoo.html.