[institut] VIII Russian Diffiety School: ANNOUNCEMENT (fwd)

[Marko Vojinovic]

------ Forwarded message ----------
Date: Wed, 24 Oct 2007 14:18:40 +0200
From: Luca Vitagliano <luca_vitagliano at fastwebnet.it>
Subject: VIII Russian Diffiety School: ANNOUNCEMENT

Dear Prof./Dr./Sir/Madam,

The Diffiety School Association is organizing the VIII Winter Diffiety 
School (Russian edition) on Geometry of Partial Differential Equations 
and Secondary Calculus, February 1-12, Kostroma (Russia). We would be 
very grateful to you if you forwarded the attached below announcement to 
all possibly interested undergraduate, graduate, PhD students, 
reasearchers and professors of your department/institution. For more 
information see the web-page of the school 
http://school.diffiety.org/page3/page0/page63/page63.html.

Thank you very much for your help
with best regards
The Organizing Committee of the VIII Winter Diffiety School (Russian 
Edition) 

###########################  ANNOUNCEMENT  ############################

          VIII Edition of the Russian Winter Diffiety School
                           Kostroma, Russia.
                        February 1 - 12, 2008.
(web page: http://school.diffiety.org/page3/page0/page63/page63.html)
  
The aim of this permanent School is to introduce undergraduate and Ph. D. 
students in Mathematics and Physics as well as post-doctoral researchers 
in a recently emerged area of Mathematics and Teoretical Physics:

                          SECONDARY CALCULUS

A diffiety is a new geometrical object that properly formalizes the 
concept of the solution space of a given system of (nonlinear) PDEs, much 
as an algebraic variety does with respect to solutions of a given system 
of algebraic equations. Secondary Calculus is a natural diffiety analogue 
of the standard calculus on smooth manifolds, and as such leads to a very 
rich general theory of nonlinear PDEs. Moreover, it appears to be a 
natural language for quantum physics, just as the standard calculus is 
the natural language for classical physics.


The school is organized in cooperation with 
- the "Bol'shaya peremena" program of Michael Batin (Kostroma, Russia);
- Istituto Italiano per gli Studi Filosofici, Italy; 

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

                               COURSES 
 
In this edition two series of courses will be given. 

B-COURSES: they are intended as courses for beginners. 

(B1) Smooth Manifolds and Observables: 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. 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. 

(B2) Symplectic, Contact Geometry and Jet Spaces: historically, 
symplectic and contact geometries were first studied as geometric 
theories of first order scalar differential equations. In particular the 
basic geometry of non-linear partial differential equations (PDEs) 
appears in its simplest form in contact geometry. Contact geometry is 
therefore an indispensable tool in understanding the structure of PDEs. 
The aim of the course is to present this non-standard point of view by 
first introducing the geometry of symplectic and contact structures and, 
finally, the analogous structures in the geometric theory of PDEs. 


A-COURSES: they are intended as advanced course for veterans and will be 
programmed later on according to the interests and backgrounds of actual 
participants. To get an idea of the may be contents check on the pages of 
the last editions of the school (the 10th Italian Edition is here on this 
site, while the other Editions can be found on the Diffiety Institute 
site). 

                              LOCATION

Kostroma 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. Detailed information about the actual location of the 
school in Kostroma and how to reach it will be duly given later on. 

                             APPLICATION

To apply, please choose among the registration forms on the web page of 
the school 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. Admitted participants will be 
informed by e-mail. The school, including a full board accomodation in 
hotel, is free for admitted participants. Travel expenses are on charge 
of participants. 

                        ORGANIZING COMMITTEE

M. Bchtold, C. Di Pietro, G. Moreno, R. Piscopo, M. M. Vinogradov, L. 
Vitagliano. 


Questions and suggestions should be sent to the e-address: 
school08ru at diffiety.ac.ru.

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

########################################################################

:-)

Marko Vojinovic
Institute of Physics
University of Belgrade
======================
e-mail: vmarko at phy.bg.ac.yu