Monsaraz and Lisbon, PORTUGAL, 1st - 10th September 1997

The main feature of noncommutative geometry is a new idea of geometric space, encoded within an algebra, noncommutative in general, instead of a set made up of points, the geometry in classical spaces being recovered when the algebra is commutative. The ordinary calculus is replaced by a new calculus of infinitesimals based on the operator formalism of quantum mechanics. The idea had its roots in the beginning of this century but has been thoroughly developed mainly in the last ten years by Alain Connes and his school giving rise to a breakthrough comparable to the non-Euclidean one. Current research includes illuminating applications to particle physics and more recently to number theory.


The sites:

1st week (1st to 6th September)

The summer school activities will take place at Convento da Orada, a spacious convent which has been totally restored a few years ago as a centre for holding seminars and small congresses and is situated in a particularly quiet place rich in megalithic monuments. Situated in the south east of Portugal, 2km from the wonderful medieval village of Monsaraz and linked to Évora by a straight road. The town of Évora is a touristic jewel recognised as a world patrimony by the UNESCO. A modern highway between Évora and Lisbon reduces the distance to about one hour by car.

2nd week (7, 8, 9, 10 September)

In the second week we move to Lisbon. Participants will be accommodated in a modern private college, not far from the Instituto Superior Técnico, the big and spacious Lisbon engineering school, where the courses will take place. During the three following days a Conference on Recent Results in Noncommutative Geometry is tentatively being organized in the same Institute, with conferences by active researchers on the topic, namely by Alain Connes, who has confirmed his presence. Since the offered prices for accomodations at Lisbon will be really accessible, the interested participants can eventually stay there these three days, at their own expenses.



International Advisory Board: A. Connes (Collège de France), S.Doplicher (Univ. La Sapienza,Roma), D.Kastler ( CPT Marseille), A.Ocneanu (Penn State).

Five introductory courses will be offered in an intensive regime:

Introduction to noncommutative geometry,by J.C. Várilly (Costa Rica)

K-theoretic tools,by G. Skandalis (Paris)

C* and von Neumann algebras, by R. Kadison (Pennsylvania)

Cyclic cohomology and local index computations, by H. Moscovici (Ohio)

The standard model in particle physics, by T. Schücker (Marseille)