[grad-students] The 9-th Diffiety school on the geometry of Partial Differential Equations

[Alan Kelm]

---------- Forwarded message ----------
From: Diffiety Scholl <school06 at diffiety.org>
To: Italian_School at diffiety.org
Date: Tue, 28 Feb 2006 14:27:11 +0300
Subject: The 9-th Diffiety school

[...]
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Dear Colleague,

we are organizing this summer from July 14 to July 31, 2006, the
ninth Diffiety School in the geometry of Partial Differential
Equations. Below you will find preliminary information about
courses, programs and other activities. We would be very grateful
to you for informing your graduate and undergraduate students,
research fellows and any other colleague who could be interested in.

On URLs
http://diffiety.ac.ru/students/its2006/9Diffiety-a3.pdf
and
http://diffiety.ac.ru/students/its2006/9Diffiety-a4.pdf
you can find the school poster in A3 and A$ formats
respectively.

More information can be found on our web sites
http://diffiety.ac.ru and http://diffiety.org

You may also wish to reply to the following address:
school06 at diffiety.org

With best regards,
         The Organizing Committee

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IX Diffiety school in the geometry of Partial Differential Equations
           Santo Stefano del Sole (Avellino),
            Italy, July 14 - 31, 2006
                   1st Announcement
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In  co-operation with
-- Diffiety Institute, Russia;
-- Istituto Italiano per gli Studi Filosofici;
-- Municipality of Santo Stefano del Sole (AV), Italy;
-- Comunita Montana Serinese-Solofrana, Italy;
-- Ente Morale S. Vito Martire, Italy,
and under the scientific direction of Prof. A. M. Vinogradov
(Salerno University, Italy, and Diffiety Institute, Russia),
we are announcing the ninth Diffiety School.

     The aim of the school is to introduce undergraduate and graduate
students in Mathematics and Physics, as well as post-doctoral
researchers and other mathematicians into a recently emerged area
of mathematics and theoretical physics:
                     Secondary Calculus
Secondary calculus is the result of a natural evolution of the
classical geometrical theory of partial differential equations (PDE)
originated by Sophus Lie.  In particular, it allows the construction
of a general theory of PDE, in the same manner as algebraic geometry
does with respect to algebraic equations.  It became also clear that
secondary calculus is a natural language for quantum field theory,
just in the same way as standard calculus is for classical physics.
>From the mathematical point of view secondary calculus is a complex
mathematical construction putting into a natural interrelation many
parts of modern mathematics such as commutative and homological
algebra, algebraic and differential topology, differential geometry,
etc.  The strategic goal of the school is to involve interested
participants into a series of large scale research programs the
Diffiety Institute is launching.

     A first idea of the area can be got from  the books:
1. Jet Nestruev, Smooth Manifolds and Observables, Graduate Texts in
    Mathematics, vol. 220, Springer-Verlag, 2002 (Russian version
    published by MCCME, Moscow, 2000).
2. Symmetries and Conservation Laws for Differential Equations of
    Mathematical Physics, Amer. Math. Soc., Translations of Mathematical Monographs,
    vol. 182, 1999 (Russian version published by Factorial, Moscow, 1997).
3. A. M. Vinogradov, Cohomological Analysis of Partial Differential
    Equations and Secondary Calculus, Amer. Math. Soc., Translations of
    Mathematical Monographs, vol.  204, 2001.

Courses:
In this edition of the school two series of courses, one for beginners
and one for the veterans, will be given. In addition, a level 3 course will be organized.

Topics for beginners are: observables, differential calculus in commutative algebras,
and analysis on manifolds.

Veterans courses will deal with modern geometric and homological methods in PDEs
(including elements of the Secondary Calculus) and their applications to integrable
systems and equations of mathematical physics.

Detailed programs will be published some later
on our web sites: http://diffiety.ac.ru and http://diffiety.org.

A scientific session aiming to involve interested participants to our research programs
is also planned.

Prerequisites:
Beginners are supposed to be familiar with fundamentals of Commutative Algebra,
Topology and Differential Geometry. For details see
http://diffiety.ac.ru and http://diffiety.org .

Organizing committee:
M. Bächtold, C. Di Pietro, V. Fiore, M. Langastro, G. Moreno, R. Piscopo, V. Vingo,
M. M. Vinogradov, L. Vitagliano.


                  Registration, accommodation, and fee.

The registration fee is expected to amount to 175 Euros. This amount may be reduced
in the future. Availability of scholarships and financial support also may present
itself. In particular, this sum assumes to cover lodging expenses. More luxurious
accommodation on the charge of participants is also possible.
Low-cost meals will be organized. Exact accommodation and payment
details will be available on May, 2006.

Interested persons are invited to fill up the registration form and return it, either
via electronic (preferable) or ordinary mail, as soon as possible, but not later
than June 30, 2006.

This web page will be constantly updated, accordingly to changes and refinements about the
details of the courses and accommodation. Interested people are therefore suggested to stay
tuned with this web site for losing no valuable information.

Addresses:
E-mail: school06 at diffiety.org

Surface mail:
Prof. A. M. Vinogradov,
Dipartimento di Matematica e Informatica,
Universita di Salerno,
Via Ponte Don Melillo,
84084 Fisciano (SA), Italy.

For registration forms and fresh school news see on our web sites
http://diffiety.ac.ru and http://diffiety.org