NONCOMMUTATIVE GEOMETRY, FEYNMAN DIAGRAMS and QUANTUM FIELD THEORY
 
 

Vienna, Austria, Erwin Schrödinger International Institute for Mathematical Physics

August 26 - November 22,

The first part of the program, devoted to
 

Feynman Diagrams in Mathematics and Physics,


will take place between August 26 and September 15.
 

The second part of the program, devoted to
 

Noncommutative Geometry and Quantum Field Theory,


will take place between September 16 and November 22.
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Feynman Diagrams in Mathematics and Physics:

Feynman diagrams provide a universal means to organize the perturbative expansion of a quantum field theory. While in some lucky cases we are
able to progress beyond the perturbative approach, it turns out that Feynman diagrams themselves are a source of fascinating mathematical problems.
They are naturally connected to configuration spaces, with their singularities located along diagonals of  coinciding vertices.
The stratification of these singularities by rooted trees, emphasized for example by Fulton and MacPherson,  makes it rather natural
that  the process of renormalization is combinatorially based on a Hopf algebra  of rooted trees that is a universal object which  contains the Hopf   algebra of iterated integrals as well as the Connes-Moscovici Hopf algebra of diffeomorphisms as sub-algebras.

It allows to relate QFT to rather unexpected branches of mathematics, remarkably including recent developments in number theory,  where the algebraic understanding of generalized polylogarithms and Euler-Zagier sums leads to the consideration of shuffle identities, Grothendieck Teichmüller groups, and
K-Z equations.

Evaluation of Feynman diagrams in recent computations  confirms the kinship between Euler-Zagier sums and those diagrams, but also emphasizes the need for a more detailed understanding of this relation.

Speakers foreseen at this moment in the Aug 26- Sep 15 period include:
 

David Broadhurst (Milton Keynes, GB)
Alain Connes (Paris, F)
Michel Dubois-Violette (Paris, F)
Boris Dubrovin (Trieste, I)
Herbert Gangl (Bonn, Germany)
Sasha Goncharov (USA)
Dirk Kreimer (Boston, USA and Paris, F)
Jean-Louis Loday (Strasbourg, F)
Martin Markl (Prague, Czech)
Werner Nahm (Bonn, Germany)
Jim Stasheff (Chapel Hill, USA)
Don Zagier (Bonn, Germany and Paris, F)
 

 
 
 
 
 
 
 

Organizer: Dirk Kreimer, Boston and Paris, and Ivan Todorov, Sofia, will stay  for at least 3 weeks covering the entire period of the activity on Feynman
diagrams from August 26 to September 15.
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Noncommutative Geometry and Quantum Field Theory:


During the last year work on the question of renormalizability of  quantum field theories defined over noncommutative algebras has been
developped with great momentum. We enjoy especially the great interest  from experts being familiar with the methods of renormalization of
undeformed quantum field theories.

Recently in particular the formulation of gauge  field theories  and their properties moved into the center of interest. In addition many questions of standard quantum field theory are now  dealt within the new framework. For example topological nontrivial  configurations like monopoles and instantons are treated within the noncommutative algebraic scheme.  The interesting connection to string  theory as well as the relations to models defined with the help of the  Born-Infeld actions are of great interest.

Besides these mentioned  topics quantum group representation theory is pushed forward. In particular, application  to the formulation of quantum group covariant models have been recently developed.
 

Speakers foreseen at this moment in the Sep 16- Nov 22 period include:

Bordemann Martin, Carey Alan, Felder Giovanni, Fiore Gaetano, Froehlich Juerg,
Gawedzki  Krzysztof,  Gracia-Bondia  Jose,  Grimstrup  Jesper,   Grosse Harald,
Jurco Branislav,  Landi   Giovanni,  Langmann  Edwin,  Madore  John,  Mickelsson
Jouko,  Moore Gregory,  Presnajder Peter,  Rajeev Sarada,  Recknagel Andreas,
Rydh  Samuel,  Schlichenmaier  Martin,  Schomerus  Volker,  Schmuedgen  Konrad,
Schlesinger  Karl-Georg,    Schupp Peter,    Schwarz  Albert,    Steinacker  Harold,
Varilly Joseph,  Wess Julius,  Wulkenhaar Raimar.

Organizer: Jouko Mickelsson, Stockholm and  John Madore, Paris will stay at ESI during extended periods in the fall of 2002. Harald Grosse stays the whole time in Vienna.

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For further information please contact: Dirk Kreimer (dkreimer@bu.edu)  (for the Aug 26-Sep 15 activities) or Harald Grosse (grosse@thp.univie.ac.at)
(for the Sep16 -Nov 22 activities) or the secretary of the Erwin Schrödinger Institute  via secr@esi.ac.at.

The scientific program including a complete list of participants and speakers will be posted on www.esi.ac.at in due time.

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December 28, 2001