EUROPEAN WOMEN IN MATHEMATICS

Workshop on
RENORMALISATION IN MATHEMATICS AND PHYSICS

Paris, 14-15 June 1996
A short report by Sylvie Paycha (coorganiser)

The purpose of this workshop was to study the various interpretations of renormalisation in dynamical systems, statistical physics, and quantum field theory, and to explore the connections among them. Preliminary discussions on this subject took place at the last EWM meeting in Madrid in September 1995.

A two day workshop on renormalisation organized jointly by Femmes et Mathématiques and EWM brought together around 20 mathematicians and physicists interested in some way or other in the concept of renormalisation.

The broad range of fields which the participants came from gives a hint as to the variety of topics both in mathematics and physics in which the concept of renormalization arises. The topics adressed during the meeting were:

• dynamical systems,
• statistical mechanics,
• quantum mechanics,
• infinite dimensional geometry.

The common drive for the participants in this meeting was to understand some of the relationships between the various interpretations of the word “renormalisation”. Each day was organised around two of the topics, the first day around dynamical systems and statistical mechanics, the second day around quantum mechanics and infinite dimesnional geometry. Some time was left for discussions between the talks to let participants discuss their points of view in an informal manner.

Two discussion sessions, one on each day, took place after the talks in order to look for common features to the different interpretations of the concept of renormalisation that had emerged during the talks that day.

The small scale of the meeting, the efforts the speakers put into trying to make their point of view understandable to non specialists and the informal discussions, all contributed to creating a pleasant atmosphere. The participants seemed to feel free to ask many questions, thus intiating stimulating discussions.

This workshop on the difficult topic of renormalisation, far from exhausting this vast area of research, hopefully helped towards a dismystification of the concept and thereby contributed to making it more accessible to non specialists present at the meeting.

The proceedings of the talks given during this meeting, complemented by an introduction reporting on some of the discussions that took place during the worshop around the concept of renormalisation, should serve as introductory material for students and non specialists.

Location.

Institut Henri Poincare, Paris, France (where femmes et mathematiques has its office).

Scientific committee

Brodil Branner, Lyngby, Denmark

Laura Tedeschini-Lalli, Rome, Italy

Sylvie Paycha, Clermont-Ferrand, France

Programme

Friday session

morning session: Renormalisation in dynamical systems (I)

speakers: Laura Tedeschini-Lalli (Rome), Betta Scoppola (Rome)

afternoon session: Renormalisation in dynamical systems (II)

speaker: Nuria Fagella (Barcelona)

Saturday session

morning session: Renormalisation in statistical mechanics and dynamical systems

speaker: Annick Lesne (Paris)

afternoon session: Extension of the notion of renormalisation to infinite dimensional geometry

speaker: Sylvie Paycha (Clermont- Ferrand)

Organising committee

Colette Guillope (Creteil, chairperson of femmes et mathematiques)

Sylvie Paycha (Clermont-Ferrand, convenor for EWM)

For further information, please contact

Sylvie Paycha

Laboratoire de Mathematiques Appliquees

Complexe Universitaire des Cezeaux

Universite Blaise Pascal
63177 Aubiere Cedex F
tel: (33) 73 40 74 42