# 07-1352/Suggested Topics for Student Lectures

 The Choices Karene $gl(1|1)$ 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.
• 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.