Levi-Civita Institute announces

WDS2009_poster_thumb IX Edition of the Russian Winter School.
Kostroma, Russia.
February 1 - 12, 2009.
Sponsored by the Foundation "Science against ages"
With the participation of the Mathematics and Mechanics Faculty of the Saint Petersburg State University
This page was originally posted on October 23, 2008.
This page is constantly updated. Please check it frequently for the latest news!


The school is organized in cooperation with

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

Contents



  2. Courses
  3. Further Activities
  4. Location
  5. Application, Selection and Admission
  6. Prerequisites
  7. Preliminary List of Admitted Participants
  8. Accommodation, Meals and Classes
  9. Organizing Committee
  10. Diffiety School Poster

Courses

In this edition of the School, four courses will be 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.
Schedule: 09:00-12:00 (actual timetable might be slightly changed).

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.
Schedule: 09:00-12:00 (actual timetable might be slightly changed).

Description: ...

Course B2.
Title: Geometric structures in the theory of PDEs.
Lecturer: Dr. Michael Bächtold.
Schedule: 09:00-11:00 (actual timetable might be slightly changed).

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 A1.
Title: Geometry of finite order jet spaces.
Lecturer: Dr. Luca Vitagliano.
Schedule: 11:00-13:00 (actual timetable might be slightly changed).

Description: ...

Course A2.
Title: Functors of differential calculus.
Lecturer: Prof. A. M. Vinogradov.
Schedule: 16:30-18:30 (actual timetable might be slightly changed).

Description: ...

Further activities


In addition, some special lectures and seminars will be organised for veterans.

Proposed talks.
The following preliminary titles have been proposed by participants. The exact schedule of the talks will be decided by the Organizing Committee and duly communicated to the speakers.



Location


Kostroma (Russian: Кострома́) is a historic city in central Russia, administrative centre of the Kostroma Oblast. A part of the Golden ring of the Russian towns, it is located at the confluence of the rivers Volga and Kostroma, 65 km east of Yaroslavl (look at the map). Detailed information about the actual location of the school in Kostroma and how to reach it will be duly given later on.

Application, Selection and Admission


To apply, please choose among the registration forms below the one which better fits your personal profile, and fill it in all its compulsory fields. Applicants will be selected by the Director of the School, prof. A. M. Vinogradov. During the selection phase, applicants may be requested to provide their curriculum and/or scientific background. Selection criteria are mainly based on the following: participants are required to be familiar with fundamentals of Commutative Algebra, Topology and Differential Geometry (see the next section: Prerequisites). Admitted participants will be duly informed by e-mail. The school, including a full board accomodation in double room in a hotel (see the section: Accommodation, Meals and Classes), is free for admitted participants. Travel expenses are on charge of participants.
DEADLINE: Application must be sent not later than Sunday, 18th of January, 2009.

Online registration for Undergraduate Students.
Online registration for Ph.D. Students.
Online registration for Post-Doctoral Students.
Online registration for Researchers and Professors.

Prerequisites


Suitable fundamentals for a fruitfull participation in the school may be found in the following references:
  • M. F. Atiyah, I. G. MacDonald, - Introduction to Commutative Algebra, - Westview Press, 1969, Chapters 1,2. A beginner participant should be able to solve exercise from these two chapters.

  • John M. Lee, - Introduction to Smooth Manifolds, - Springer-Verlag, Graduate Texts in Mathematics, Vol. 218, 2003. Appendix + Chapters 1-4, 6 (Chapter 1 is also available on the author's web page).

  • Jet Nestruev, - Smooth manifolds and Observables . - Springer-Verlag, Graduate Texts in Mathematics, Vol. 220, 2002. First chapters of this book will introduce you to the spirit of the school.
People who have read this book and solved 70% of the exercises will be able to follow the veteran courses.

Preliminary list of admitted participants

Admitted participants are listed below accordingly to the time of their application. Such a list is regularly refreshed (last update: January 23, 2009).
  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. Paul Alexandru Zah (Constanta, ROMANIA) - University of Aberdeen;
  10. Sergey Nikolayevich Uksusov (Voronezh, RUSSIA) - Voronezh State University;
  11. El Hassan El Kinani (Erracchidia, MOROCCO) - Faculté des Sciences et Technique Errachidia;
  12. Marina Iljina (Tambov, RUSSIA) - Derzhavin Tambov State University;
  13. Denis Tugaryov (Tambov, RUSSIA) - Derzhavin Tambov State University;
  14. Eugeniy Dinvay (St. Petersburg, RUSSIA) - St. Petersburg State University;
  15. Maria Sorokina (St. Petersburg, RUSSIA) - St. Petersburg State University;
  16. Irina Gorbunova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  17. Andrey Krutov (Shuya (Ivanovo), RUSSIA) - Ivanovo State Power University;
  18. Andrey Yuyukin (Voronezh, RUSSIA) - Voronezh State University;
  19. Nina Belyajeva (Voronezh, RUSSIA) - Voronezh State University;
  20. Elena Korchagina (Voronezh, RUSSIA) - Voronezh State University;
  21. Anastasiya Men'shikh (Voronezh, RUSSIA) - Voronezh State University;
  22. Natalia Pritykovskaya (St. Petersburg, RUSSIA) - St. Petersburg State University;
  23. Ivan Kobyzev (St. Petersburg, RUSSIA) - St. Petersburg State University;
  24. Fedor Sandomirskiy (St. Petersburg, RUSSIA) - St. Petersburg State University;
  25. Ekaterina Golikova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  26. Azat Tagirdzhanov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  27. Svetlana Vangesova (Zürich, SWITZERLAND) - St. Petersburg State University;
  28. Vyacheslav Kalnitsky (St. Petersburg, RUSSIA) - St. Petersburg State University;
  29. Mikhail Khristoforov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  30. Xenia Chernysh (St. Petersburg, RUSSIA) - St. Petersburg State University;
  31. Alexander Igamberdiev (St. Petersburg, RUSSIA) - St. Petersburg State University;
  32. Maria Nikanorova (St. Petersburg, RUSSIA) - St. Petersburg State University;
  33. Svetlana Azarina (Voronezh, RUSSIA) - Voronezh State University.

Accommodation, Meals and Classes

Participants will lodge in double room and have meals in the

Sanatorij "Kostromskoj" (Russian: Санаторий Костромской),
micro-rajon Malyshkovo,
156011 Kostroma, RUSSIA.
Look at the map ("micro-rajon Malyshkovo" is not indicated: it is the left branch at the end of ул. Малышковская).
Exact geographical coordinates are: 57°43'45" N, 40°55'27" E, 117m a.s.l., planet Earth.
You may also be interested at the Russian web site.

Arrival day is Saturday, 31 of January, and departure day is Friday, 13 of February, 2009.
Classes and seminars will take place in the Sanatorij itself in the days from 1 to 12 of February, 2009. A detailed schedule of the school activities will be published later.

Organizing committee


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

Questions and suggestions should be sent to the e-address:
school09ru

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 here for download.