WDS2009_poster_thumb IX Edition of the Russian Winter School.
Kostroma, Russia.
February 1 - 12, 2009.
Under the auspices of Levi-Civita Institute.
Sponsored by the Foundation "Science against ages"
With the participation of the Mathematics and Mechanics Faculty of the Saint Petersburg State University

DiffeoCraziness-2
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. List of Participants
  3. Passed Exams
  4. Organizing Committee

Courses

In this edition of the School, six courses was proposed.
The general classification of Diffiety School's courses is as follows:

B-COURSE(S): courses for beginners;
A-COURSE(S): advanced courses;
C-COURSE(S): courses for veteran participants.

Course B0.
Title: Introduction to differential calculus over commutative algebras.
Lecturer: Prof. A. M. Vinogradov.

Description: course B0 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. As a key example, calculus over smooth manifolds will be developed according to this philosophy, i.e., "algebraically". Hence it will be shown that differential geometry can be developed over an arbitrary commutative algebra as well. Course B0 is recommended, first of all, to undergraduate students of the second and the third years and, more generally, to those whose algebraic background is limited. B0 is designed as a unique course for those who will attend it and will be accompained by numerous exercises one part of which will be discussed in the class and another one will take part of the final exam.

Course B1.
Title: First order calculus on smooth manifolds.
Lecturer: Dr. Giovanni Moreno.

Course B2.
Title: Geometric structures in the theory of PDEs.
Lecturer: Dr. Michael Bächtold.

Description: the course will start with simple examples of non-linear partial differential equations (PDEs) that show in which circumstances symplectic and contact geometries were invented as theories revealing basic structures of first order non-linear PDEs. The general theory of nonlinear PDEs is in a sense a very nontrival generalization of contact geometry and as such is an indispensable first step in understanding the structure of PDEs. Symplectic geometry is a symmetry reduction of contact geometry which is the mathematical basis of most important contemporary physical theories. So, this geometry and the related Hamiltonian formalism are indispensable as the starting point in understandig what mathematics should be developed in order to face basic problems in contemporary physics and mechanics.

Course A0.
Title: Linear connections on vector bundles.
Lecturer: Dr. Luca Vitagliano.

Course A1.
Title: Geometry of finite order jet spaces.
Lecturer: Dr. Luca Vitagliano.

Course A2.
Title: Functors of differential calculus.
Lecturer: Prof. A. M. Vinogradov.

List of participants

People who participated to the School are listed below.
  1. Jet Nestruev (Moscow, RUSSIA, and Salerno, ITALY) - Levi-Civita Institute;
  2. Daria Nikishina (Voronezh, RUSSIA) - Voronezh State University;
  3. Julia Popova (Voronezh, RUSSIA) - Voronezh State University;
  4. Valeria Samoilova (Voronezh, RUSSIA) - Voronezh State University;
  5. Alexandra Yasmenko (Voronezh, RUSSIA) - Voronezh State University;
  6. Thomas Leuther (Aubel, BELGIUM) - Université de Liège;
  7. Monika Stypa (Przylek, POLAND) - University of Lublin;
  8. Fan Wu (Beijing, P. R. CHINA) - Capital Normal University;
  9. Marina Iljina (Tambov, RUSSIA) - Derzhavin Tambov State University;
  10. Denis Tugaryov (Tambov, RUSSIA) - Derzhavin Tambov State University;
  11. Eugeniy Dinvay (St. Petersburg, RUSSIA) - St. Petersburg State University;
  12. Maria Sorokina (St. Petersburg, RUSSIA) - St. Petersburg State University;
  13. Irina Gorbunova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  14. Andrey Krutov (Shuya (Ivanovo), RUSSIA) - Ivanovo State Power University;
  15. Andrey Yuyukin (Voronezh, RUSSIA) - Voronezh State University;
  16. Nina Belyajeva (Voronezh, RUSSIA) - Voronezh State University;
  17. Elena Korchagina (Voronezh, RUSSIA) - Voronezh State University;
  18. Anastasiya Men'shikh (Voronezh, RUSSIA) - Voronezh State University;
  19. Natalia Pritykovskaya (St. Petersburg, RUSSIA) - St. Petersburg State University;
  20. Ivan Kobyzev (St. Petersburg, RUSSIA) - St. Petersburg State University;
  21. Fedor Sandomirskiy (St. Petersburg, RUSSIA) - St. Petersburg State University;
  22. Ekaterina Golikova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  23. Azat Tagirdzhanov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  24. Vyacheslav Kalnitsky (St. Petersburg, RUSSIA) - St. Petersburg State University;
  25. Mikhail Khristoforov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  26. Xenia Chernysh (St. Petersburg, RUSSIA) - St. Petersburg State University;
  27. Alexander Igamberdiev (St. Petersburg, RUSSIA) - St. Petersburg State University;
  28. Maria Nikanorova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  29. Svetlana Azarina (Voronezh, RUSSIA) - Voronezh State University.

Passed exams



Course B0.
The following participants successfully passed the examination:
  1. Denis Tugaryov;
  2. Irina Gorbunova;
  3. Natalia Pritykovskaya;
  4. Ivan Kobyzev;
  5. Eugeniy Dinvay.
Course B1.
The following participants successfully passed the examination:
  1. Mikhail Khristoforov;
  2. Xenia Chernysh;
  3. Alexander Igamberdiev.

Course A0.
The following participants successfully passed the examination:
  1. Fan Wu.

Course A1.
The following participants successfully passed the examination:
  1. Thomas Leuther.


Organizing committee


M. Bächtold, V. Kalnitsky, G. Moreno, M. M. Vinogradov, L. Vitagliano.

Questions and suggestions should be sent to the e-address:

school09ru