07-1352/Suggested Topics for Student Lectures

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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.
  • 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 anywhere else.