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11-Diffiety-poster_thumb XI Edition of the Italian Summer School.
Santo Stefano del Sole (Avellino), Italy.
July 17 - August 1, 2008.

The school was organized in cooperation with

and under the scientific direction of Prof. A. M. Vinogradov (Università di Salerno, Italy, and Diffiety Institute, Russia).

Contents



  1. Courses
  2. Talks
  3. List of Participants
  4. Organizing Committee
  5. Diffiety School Poster
  6. Press Release
  7. Photo Gallery

Courses


09:00-10:50 B1 (A. Vinogradov) C (L. Vitagliano)
10:50-11:10 COFFEE BREAK
11:10-13:00 B2 (G. Moreno) A (A. Vinogradov)


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Course B1.
B1
Title: Observability in Physics and Differential Calculus over Commutative Algebras.
Lecturer: Prof. Alexandre M. Vinogradov.
Schedule: 1h50' per day (from 09:00 to 10:50).

Description: The course aims to show that the natural language of classical physics is differential calculus over commutative algebras and that this fact is a consequence of the classical observability mechanism. From mathematical side this allows to reveal the "logic" of differential calculus. Indeed, differential calculus is the study of certain functors, their representative objects and natural transformations in suitable categories of modules over commutative algebras. On the base of this study all differential geometric concepts may be formalized over an arbitrary commutative algebra. Differential calculus over commutative algebras is not only the "mathematical grammar" of classical nature but it is an indispensable tool in Secondary Calculus.

List of attendees:

  • Reza Aghayan;
  • Stephan W. Anzengruber;
  • Jenny Santoso;
  • Zain Ulabidin Shaikh;
  • Ildar Sharafutdinov;
  • Vladimir Suvorov;
  • Egor Valerevich Zarubin;
  • Alexander Zotikov;
  • Thomas Leuther.

Diplomas delivered to:

  • Reza Aghayan;
  • Zain Ulabidin Shaikh;
  • Thomas Leuther.


Course B2.
B2
Title: First Order Calculus on Smooth Manifolds.
Lecturer: Dr. Giovanni Moreno.
Schedule: 1h50' per day (from 11:10 to 13:00).

Description: Calculus over smooth manifolds will be developed according to the philosophy of course B1, i.e., "algebraically". It will be shown that even in basic differential geometry, this approach reveal more details than the standard one. This course is propedeutic for further more advanced courses concerning both the geometry of PDEs and Secondary Calculus.

List of attendees:

  • Stephan W. Anzengruber;
  • Jenny Santoso;
  • Vladimir Suvorov.

Diplomas delivered to:

  • Stephan W. Anzengruber.


Course A.
Title: Geometry of Finite Order Jet Spaces.
Lecturer: Prof. Alexandre M. Vinogradov.
Schedule: 1h50' per day (from 11:10 to 13:00).

Description: The functional analytic approach to differential equations hides the basic natural structures of PDEs. On the other side they clearly appears in the geometric approach based on the theory of jet spaces. First of all, the basic geometrical structures on jet spaces will be discussed in the perspective of the subsequent passage to infinite jets. In particular, it will be explained what really PDEs are from the modern point of view, what are their classical symmetries, singularities of their solutions, etc.

List of attendees:

  • Reza Aghayan;
  • Svetlana Azarina;
  • Stanislav Dubrovskiy;
  • prof. Tadeusz Jagodzinski;
  • Victor Erikovich Kasatkin;
  • Antonio Nigro;
  • Zain Ulabidin Shaikh;
  • Elizaveta Gennadievna Vishnyakova.

Diplomas delivered to:

  • Reza Aghayan;
  • Victor Erikovich Kasatkin ;
  • Antonio Nigro;
  • Zain Ulabidin Shaikh.


Course C.
C
Title: Secondary Differential Forms and Vector Fields.
Lecturer: Dr. Luca Vitagliano.
Schedule: 1h50' per day (from 09:00 to 10:50).

Description: The aim of the course is to introduce the category of diffieties and the fundamentals of Secondary Calculus on the base of the C-Spectral Sequence whose first term is naturally interpreted as the space of differential forms on the "solution manifold" of a system of (nonlinear) PDEs. It will be proved that calculus of variations, conservation laws theory, etc., are just small aspects of C-spectral sequence theory.

List of attendees:
  • Svetlana Azarina;
  • Stanislav Dubrovskiy;
  • prof. Tadeusz Jagodzinski;
  • Victor Erikovich Kasatkin;
  • prof. Olga Veniaminovna Kunakovskaya;
  • Antonio Nigro;
  • Elizaveta Gennadievna Vishnyakova.

Diplomas delivered to:

  • Svetlana Azarina;
  • Victor Erikovich Kasatkin;
  • Elizaveta Gennadievna Vishnyakova.


List of participants


Participants are listed below accordingly to the time of their application.

  1. Jet Nestruev (Moscow, RUSSIA and Salerno, ITALY);
    Elizaveta Gennadievna
    Vishnyakova (Tver', RUSSIA) - Tver State University;
  2. Reza Aghayan (Tehran, IRAN) - Iran University of Science and Technology;
  3. Stanislav Dubrovskiy (Be'er Sheva, ISRAEL) - Ben Gurion University;
  4. Antonio Nigro (Turin, ITALY) - Politecnico Di Torino;
  5. prof. Olga Veniaminovna Kunakovskaya (Voronezh, RUSSIA) - Voronezh State University;
  6. Svetlana Azarina (Voronezh, RUSSIA) - Voronezh State Technical University;
  7. prof. Viacheslav Stepanovich Kalnitskiy (St. Petersburg, RUSSIA) - St. Petersburg State University;
  8. Egor Valerevich Zarubin (St. Petersburg, RUSSIA) - St. Petersburg State University;
  9. Jenny Santoso (Stuttgart, GERMANY) - University of Stuttgart;
  10. Alexander Zotikov (St. Petersburg, RUSSIA) - SPbGU;
  11. Ildar Sharafutdinov (Ufa, RUSSIA) - St. Petersburg State University;
  12. prof. Tadeusz Jagodzinski (Warsaw, POLAND) - Mathematics and Information Techniques Faculty;
  13. Stephan W. Anzengruber (Linz, AUSTRIA) - Research Institute for Computational and Applied Mathematics (RICAM);
  14. Thomas Leuther (Aubel, BELGIUM) - University of Liege;
  15. Victor Erikovich Kasatkin (St. Petersburg, RUSSIA) - St. Petersburg State University;
  16. Zain Ulabidin Shaikh (Aberdeen, UK) - University of Aberdeen;
  17. Vladimir Suvorov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  18. prof. Alexander Florinsky (St. Petersburg, RUSSIA) - St. Petersburg State University;
  19. prof. Wiesław Sasin (Warsaw, POLAND) - Warsaw University of Technology;

Talks


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During the School the following talks were given:
  • Sunday, July 27: "Moduli space of general connections", by Stanislav Dubrovskiy;
  • Monday, July 28: "A jet space construction that reproduces the Dorfman Bracket", by Zain Shaikh;
  • Tuesday, July 29: "0- and 1-cohomology of tangent sheaf on supermanifolds of flags", by Elizaveta Vishnyakova.


Organizing committee


M. Bächtold, C. Di Pietro, V. Fiore, V. Kalnitsky, M. Langastro, G. Moreno, C. Ragano, M. M. Vinogradov, L. Vitagliano, M. Y. Zvagelsky.

The Organizing Committee can be contacted for any question and suggestion via the e-address:
school08it

Diffiety School poster


The Organizing Committee expresses its gratitude to those who spread the news about the School in their University/Department, by displaying the official poster. A PDF electronic copy of it is available for download.

Press Release


Information about the School appeared on local and national newspapers. Click here to access the electronic copies.

Photo Gallery

Photo gallery is constantly updated. Click here to visit it.
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