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

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 $gl(1|1)$ 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.