07-1352/Suggested Topics for Student Lectures

07-1352/Navigation Panel   Back to 06-1350 # Week of... Links 1 Jan 9 About, Notes 2 Jan 16 Notes 3 Jan 23 Notes 4 Jan 30 Notes and Plans 5 Feb 6 Notes 6 Feb 13 Notes R Feb 20 Reading week 7 Feb 27 Notes 8 Mar 6 Notes 9 Mar 13 Notes 10 Mar 20 Notes 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	$gl(1|1)$
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.

• 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 $gl(1|1)$ 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 Dror's EMP paper.

• Anything else from VasBib.

• Anything else from anywhere else.