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 47, 2000
University of Aarhus
In the abovementioned 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
Time  Tuesday  Wednesday  Thursday  Friday 
9.1510.15 
registration 
10.1511.00 
Lectures  Lectures  Lectures  Exercises 
11.1512.00 
Lectures  Lectures  Lectures  Exercises 
LUNCH (from 12.30) 
14.1515.00 
Lectures  Exercises   Lectures 
15.1516.00 
Lectures  Exercises  Lectures  Lectures 
16.1517.00 
  Lectures  
Lecture notes
The lecture notes for the course may be downloaded in
[ postscript 
pdf ]
format.
List of participants
 Bedia Akyar (Aarhus)
 Jørgen Ellegaard Andersen (Aarhus)
 William Browder (Princeton)
 Marcel Bökstedt (Aarhus)
 Johan Dupont (Aarhus)
 Jakob Grove (Aarhus)
 Søren Have Hansen (MaPySto, Aarhus)
 Søren Kold Hansen (Aarhus)
 Lars Hesselholt (MIT)
 Herbert Lee (MaPySto, Copenhagen)

 Ib Madsen (Aarhus)
 Takuro Mochizuki (Osaka)
 Tetsuhiro Moriyama (RIMS, Kyoto)
 Maciej Mroczkowski (Uppsala)
 Holger Andreas Nielsen (Aarhus)
 Henrik Hald Nørgaard (Aarhus)
 Anders Skov (Aarhus)
 Erik Skibsted (Aarhus)
 Jørgen Tornehave (Aarhus)
 Pierre Vogel (Paris VII)
 Henrik Vosegaard (Aarhus)

Related
More Information
Do not hesitate to contact the MaPhySto secretariat
(at maphysto@maphysto.dk
)
or the local organizer
Jørgen
Ellegaard Andersen
for further information.
This document,
http://www.maphysto.dk/oldpages/events/VogelCAC2000/index.html,
was last modified
January 19, 2004.
Questions or comments to the contents of this document should
be directed to
maphysto@maphysto.dk.