Santo Stefano del Sole (Avellino),
Italy,

July 19 - 31, 2002

This school was organized also in cooperation with

- Istituto Italiano per gli Studi Filosofici

- Municipality of Santo Stefano del Sole (AV), Italy

and under the scientific direction of Prof. A. M. Vinogradov (Universita' di Salerno, Italy, and Diffiety Institute, Russia). The aim of the school was to introduce undergraduate and graduate students in Mathematics and Physics, as well as post-doctoral researchers and other mathematicians into a recently emerged area of mathematics and theoretical physics:

The strategic goal of the school is to involve interested participants into a series of large scale research programs the Diffiety Institute is launching.

A first idea of the area can be got from the books:

*Symmetries and Conservation Laws for Differential Equations of Mathematical Physics.*- AMS, Mathematical Monographs, volume 182, 1999.- A. M. Vinogradov:
*Cohomological Analysis of Partial Differential Equations and Secondary Calculus*. - AMS, Mathematical Monographs, volume 204, 2001. - J. Nestruev:
*Smooth manifolds and Observables*-. MCCME, Moscow, 2000 (in Russian); Springer-Verlag, New York, 2002 (in English), Graduate Texts of Mathematics series.

In this edition of the school the following two courses was given:

- Differential Calculus over Commutative Algebras and Smooth Manifolds (suggested to beginners).
- Infinite Jets and Diffieties (suggested to more experienced participants).

During the School there was discussed the following starting programs, intended to involve interested participants into our research projects:

**"Einstein";****Singular Lagrangians and Hamiltonian formalism;****Differential Invariants: theory and applications;****Towards Differential Algebraic Geometry.**

Also there was organized a scientific session on the base of research interests of the participants.

** Lecturers and tutors in the School**:

- A. De Paris (Universita' "Federico II" di Napoli)
- S. Igonin (Independent University of Moscow)
- A. Verbovetsky (Independent University of Moscow, Diffiety Institute)
- A. Vinogradov (Universita' di Salerno, Diffiety Institute)
- M. Vinogradov (Diffiety Institute)
- R. Vitolo (Universita' di Lecce, Diffiety Institute)

Organizing committee:

D. Catalano Ferraioli, A. De Paris, C. Di Pietro, G. Manno, R. Piscopo, F. Pugliese, G. Rotondaro, F. Strazzullo, R. Vitolo.

List of participants:

- Gianni Manno (King's College London)
- Diego Catalano (University of Salerno)
- Christian Di Pietro (University of Naples)
- Francesco Strazzullo (University of Naples)
- Rossella Piscopo (University of Naples)
- Valentina Golovko (University of Moscow)
- Leonid Stunzhas (University of Moscow)
- Angela Cardone (University of Naples)
- Antonio De Nicola (University of Naples)
- Daniele Signori (University of Milano)
- Ida Del Prete (University of Naples)
- Jan Tuitman (University of Groningen)
- Luca Vitagliano (University of Roma)
- Nicola Carchia (University of Naples)
- Prof. Georges G. Weil (Polytechnic University of New York)
- Rink Hallmann (Univerity of Twente)
- J.H. Sikkema (University of Groningen)
- Silvana Martucci (University of Salerno)
- Giovanni Moreno (University of Naples)
- Giovanni Sburlati (University of Turin)