MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

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Funded by The Danish National Research Foundation

Concentrated Advanced Course on

Vassiliev invariants, chord diagrams, the Kontsevich integral, the structure of the algebra of Feynman diagrams, and the universal Lie algebra

Lectures by Pierre Vogel (Paris VII)

January 4-7, 2000

University of Aarhus

In the above-mentioned period, MaPhySto organized Concentrated Advanced Course on these topics within the area of geometric mathematical physics. The course took place at the Department of Mathematical Sciences, University of Aarhus.

Course Contents

Vassiliev theory:

Invariants of knots or links, Vassiliev invariants, singular links and chord diagrams. The Vassiliev filtration on the space of links and its relation with the module of chord diagrams.

Trivalent Feynman diagrams:

The AS and IHX relations. Basic facts about modules of trivalent diagrams ${\cal A}(\Gamma,X)$.

The Kontsevich integral:

Description of the integral. The isomorphism (after completion) between the modules of knots and the graded modules of trivalent diagrams ${\cal A}(S^1,\emptyset)$.

Structure of the module ${\cal A}(\Gamma,X)$:

Coalgebra structure and functoriality. The algebra $\Lambda$ and its action on modules of diagrams. Weight functions coming from Lie algebras. The height characters corresponding to all Lie algebras and Lie superalgebras.

The universal Lie algebra:

Construction of this universal object. Known facts and conjectures about it: the category of representations, simple modules and their dimensions.

Schedule

Lecture notes

The lecture notes for the course may be down-loaded in [ postscript | pdf ] format.

List of participants

Related

• Pierre Vogel's home-page
• 1999 Summer School on Invariants of links and 3-manifolds

More Information

Do not hesitate to contact the MaPhySto secretariat (at maphysto@maphysto.dk) or the local organizer Jørgen Ellegaard Andersen for further information.