Dear Sir/Madam/Dr./Prof.
we apologize if you already received this e-mail

The Diffiety School Association is organizing the XI Summer Italian
Diffiety School on Geometry of Partial Differential Equations and
Secondary Calculus, July 17 - August 1, 2008, Santo Stefano del Sole (AV)
Italy. 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/page64/page64.html.

Thank you very much for your help
with best regards
The Organizing Committee of the XI Summer Italian Diffiety School

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

     XI EDITION OF THE SUMMER ITALIAN DIFFIETY SCHOOL
School in Geometry of Partial Differential Equations and Secondary Calculus
                  Santo Stefano del Sole (Avellino), Italy.
                         July 17 - August 1, 2008.

The aim of the permanent Diffiety 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

Diffiety Institute (Russia);
Istituto Italiano per gli Studi Filosofici (Italy);
Dipartimento di Matematica e Informatica, UniversitЮ degli Studi di
Salerno (Italy);
Municipality of Santo Stefano del Sole (Italy);
ComunitЮ Montana Serinese-Solofrana (Italy) ;
Ente Morale S. Vito Martire (Italy);

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

CONTENTS OF THE ANNOUNCEMENT

Courses
Application, Selection and Admission
Registration fee
Prerequisites
Accommodation, Meals and Classes
Free day
Organizing Committee
Diffiety School Poster
Location

COURSES

In this edition of the School, the standard courses for beginners will be
proposed.
Advances courses and courses for veterans will be announced later on (look
at past editions for more information about such courses).
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 B1.
Title: Smooth manifolds and observables.
Lecturer: TBA.

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.
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 B2.
Title: Geometric structures in the theory of PDEs.
Lecturer: TBA.

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.

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

APPLICATION, SELECTION AND ADMISSION

To apply, please choose among the registration forms you find at the
webpage of the school
http://school.diffiety.org/page3/page0/page64/page64.html 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.

DEADLINE: TBA.

REGISTRATION FEE

The registration fee of the school, including a full board (except for the
meals of the free day) accommodation (see the section: Accommodation,
Meals and Classes), amounts to 175 EUR. Travel expenses are on charge of
participants.
Participants coming from Eastern Europe might take advantage of EMS
scholarships.
Registration fee can be paid cash upon arrival or by wire transfer
directly to Diffiety School's bank account:

IBAN: IT82N0539203404000001274373
ACCOUNT NAME: DIFFIETY SCHOOL
BANK: BANCA DELLA CAMPANIA
BRANCH: AGENZIA NAPOLI 4

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.

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.

ACCOMODATIONS, MEALS AND CLASSES

Men will lodge in very spartan dormitories with shared bathrooms. Women
will lodge in some apartment(s) made available by the Municipality of
Santo Stefano del Sole.
Interested people can contact the Organizing Committee about the
availability of more luxurious accommodation, on their charge.
The hotel "Il Ciliegio" is the only high-standard lodging solution
available in the neighborhoods, located just 1500 meters away from the
center of Santo Stefano del Sole (look at the map). Interested people can
contact the hotel to book their own rooms, introducing themselves as
participants to the School.
The non-EU participants will be asked, during the first days of the
school, for their cooperation to carry out the compulsory registration
procedure at the Police's designated office.

Meals are served to participants in the elementary school's refectory
located on the intersection of "Via Colacurcio" and "Via Pisacreta" (look
at the map), one level above the bar. Breakfast is served at 08:00, lunch
at 13:30 and supper at 21:30.

On the arrival day (July 17) only supper is served.
On the departure day (August 1) only breakfast is served
On the free day (July 24) no meals are served.

Classes take place every morning from July 18 to July 23 and from July 25
to July 30 in the "Aula Consiliare" (counsel room) of the Municipality of
Santo Stefano del Sole, just 500 meters away from the center (look at the
map). Seminars, talks and other scientific activities will take place
there in the afternoons, and diploma delivery and closing ceremony will be
organized there on the last day (July 31).

FREE DAY

On Thursday, July 24, the School activity is suspended. Participants are
free to visit the neighborhoods, to remain in Santo Stefano del Sole, or
to take part to one of the guided excursions which will be proposed by the
Organizing Committee. More information about excursion(s) will be duly
announced on the web page of the school
http://school.diffiety.org/page3/page0/page64/page64.html.
People who intend to go away from Santo Stefano del Sole during the free
day and plan their own itinerary, should keep in mind that the buses from
Avellino to Santo Stefano del Sole leave at 07:50, 10:10, 11:10, 12:10,
13:10, 14:30, 16:00, 17:30, 18:30 and 20:00.

ORGANIZING COMMITTEE

M. BДchtold, C. Di Pietro, V. Fiore, V. Kalnitsky, M. Langastro, G.
Moreno, R. Piscopo, 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.ac.ru

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 at
the webpage of the school
http://school.diffiety.org/page3/page0/page64/page64.html.

LOCATION

Santo Stefano del Sole is a small (about 2100 inhabitants) village
located in the heart of a mountainy region called "Irpinia". Its
territory begins 328 meters above the sea level and stretches over the
shoulders of the hills untill it reaches 1146 meters, covering more than
ten square kilometers, half of which is forest. You may find many shots
of the school location at the webpage of the X Edition of Summer Diffiety
School http://school.diffiety.org/page3/page4/page48/page48.html.
Exact geographical coordinates are: 40╟54' N, 14╟51' E, 510m a.s.l.,
planet Earth.
Reaching Santo Stefano del Sole is quite easy. You may find detailed
instruction at the web page of the school
http://school.diffiety.org/page3/page0/page64/page64.html.

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