Diffiety School




The Diffiety School has been created in 1998 under the auspices of

Scientific Director: A. M. Vinogradov (Universita'; di Salerno)

Scientific Committee:
C. Becchi (Universita' di Genova)
J. Krasil'shchick (Universita' Indipendente di Mosca)
G. Marmo (Universita' "Federico II" di Napoli)
A. M. Vinogradov (Universita' di Salerno)


  1. On the School
  2. Next edition of the School
  3. Teachers and Organisers of the School
  4. Our address

On the School

The aim of the School is to form a research team in order to explore a recently emerged area in Mathematics and Physics:
Secondary Calculus and Cohomological Physics,

which is going to be of fundamental importance in the near future.

The intention is to bring together undergraduate and graduate students in Mathematics and Physics, as well as post-doctoral researchers and other (young in spirit...) mathematicians to perform a vast joint research program , ranging from functors of differential calculus over commutative algebras to secondary calculus over diffieties. Important applications of these new methods are expected in traditional areas of mathematics such as homological algebra, Lie groups and algebras, algebraic geometry, differential geometry, differential equations, and in applications, such as classical and quantum mechanics, mechanics of continuous media, classical and quantum field theory.

The School has been divided into several editions that take the students from the very beginning of commutative algebra and differential geometry to a research level. Our first task is to introduce students to the language of Differential Calculus on Commutative Algebras. Next, we introduce the geometry of infinite jet spaces and diffieties.

During the School, several possible reserch arguments of any level will be proposed to interested participants. This will also be an occasion to start a scientific interchange and a cooperation between research groups of other Universities and our group.

After the School, close contact with interested participants will be mantained through our local weekly seminar. Research material from the seminar will be available from our site, as well as lecture notes from the editions of the School.

Three editions of the School have been performed until now.
The first one has been held in Pereslavl'-Zalessky, near Moscow, in 1998, and repeated in Forino, near Salerno, in the same year. The main subjects of this edition were basic commutative algebra and differential geometry. From the very beginning manifolds were introduced as spectra of algebrae.
The second one has been held in 1999 in the same places. The main subjects were algebraic topology, cohomological theory of integration and basic theory of jet spaces.
The third one has been held in Pereslavl'-Zalessky in Summer 2000. The courses introduced the geometric theory of P.D.E. and their symmetries.

A new edition of the school is currently being organized in Forino from 17 to 29 July 2000. Check here for more information.

Teachers and Organizers of the School

Here follows the list of teachers and tutors in the School:

A. M. Vinogradov, Director (Universita' di Salerno)
V. Chetverikov (Technical University of Moscow)
A. De Paris (Universita' "Federico II" di Napoli)
S. Igonin (Independent University of Moscow)
M. Marvan (Silesian University at Opava, Czech Rep.)
A. Verbovetsky (Independent University of Moscow)
M. Vinogradov (Diffiety Institute, Russia)
R. Vitolo (Universita' di Lecce)
V. Yumaguzhin (University of Pereslavl'-Zalessky, Russia)

And here's the organising committee:
C. Bove, F. Canfora, D. Catalano, S. Cioffi, A. De Paris, G. Manno, B. Prinari, F. Pugliese, L. Vitagliano, R. Vitolo.


Interested people can contact the Diffiety School at the following address:

Prof. A. M. Vinogradov, Universita' degli Studi di Salerno, Facolta' di Scienze, Dipartimento di Matematica e Informatica, Via Salvatore Allende, 84081 Baronissi (Salerno).

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