[institut] Announcement - XII Summer Diffiety School (fwd)

Fri Nov 14 13:01:00 CET 2008

---------- Forwarded message ----------
Date: Fri, 14 Nov 2008 10:44:43 +0100
From: Luca Vitagliano <lvitagliano at unisa.it>
Subject: Announcement - XII Summer Diffiety School

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

The Levi-Civita Institute (www.levi-civita.org) is organizing the

XII EDITION OF THE SUMMER ITALIAN DIFFIETY SCHOOL

on Geometry of Partial Differential Equations and Secondary Calculus, 
July 16-31, 2009, 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, Ph.D. 
students, reasearchers and professors of your department/institution.

For more information see the web-page of the school 
http://school.diffiety.org/page3/page0/page93/page93.html

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

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

XII EDITION OF THE SUMMER ITALIAN DIFFIETY SCHOOL

School in Geometry of Partial Differential Equations and Secondary Calculus
               Santo Stefano del Sole (AV), Italy.
                      July 16-31, 2009.

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. It appears that it is this the 
only natural language of quantum physics, just as the standard Calculus 
is for classical physics.

The school is organized in cooperation with

Istituto Italiano per gli Studi Filosofici - Italy (www.iisf.it); 
Municipality of Santo Stefano del Sole - Italy 
(www.comune.santostefanodelsole.av.it);
Dipartimento di Matematica e Informatica, Università degli Studi di 
Salerno - Italy (www.dmi.unisa.it);
Ente Morale S. Vito Martire, Italy.

And under the scientific direction of Prof. A. M. Vinogradov (Università 
di Salerno, Italy, and Levi-Civita Institute, Italy).

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.

Here is a tentative list of courses that will be activated this year

Course B1. 
Title: Observability in Physics and Differential Calculus over Commutative Algebras. 
Lecturer: TBA. 
Schedule: 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. 
From mathematical side this allows to reveal the "logic" of differential 
calculus. Indeed, differential calculus is the study of certain functors, 
their representative objects and natural transformations in suitable 
categories of modules over commutative algebras. On the base of this 
study all differential geometric concepts may be formalized over an 
arbitrary commutative algebra. Differential calculus over commutative 
algebras is not only the "mathematical grammar" of classical nature but 
it is an indispensable tool in Secondary Calculus. 

Course B2. 
Title: First Order Calculus on Smooth Manifolds. 
Lecturer: TBA. 
Schedule: TBA. 

Description: Calculus over smooth manifolds will be developed according 
to the philosophy of course B1, i.e., "algebraically". It will be shown 
that even in basic differential geometry, this approach reveal more 
details than the standard one. This course is propedeutic for further 
more advanced courses concerning both the geometry of PDEs and Secondary 
Calculus.

Course A. 
Title: Geometry of Finite Order Jet Spaces. 
Lecturer: TBA. 
Schedule: TBA. 

Description: The functional analytic approach to differential equations 
hides the basic natural structures of PDEs. On the other side they 
clearly appears in the geometric approach based on the theory of jet 
spaces. First of all, the basic geometrical structures on jet spaces will 
be discussed in the perspective of the subsequent passage to infinite 
jets. In particular, it will be explained what really PDEs are from the 
modern point of view, what are their classical symmetries, singularities 
of their solutions, etc.

Course C. 
Title: Secondary Differential Forms and Vector Fields. 
Lecturer: TBA. 
Schedule: TBA. 

Description: The aim of the course is to introduce the category of 
diffieties and the fundamentals of Secondary Calculus on the base of the 
C-Spectral Sequence whose first term is naturally interpreted as the 
space of differential forms on the "solution manifold" of a system of 
(nonlinear) PDEs. It will be proved that calculus of variations, 
conservation laws theory, etc., are just small aspects of C-spectral 
sequence theory. 

look at past edition web-pages 
http://school.diffiety.org/page3/page4/page4.html for more information

Further activities.
For veterans are planned some additional activities (seminars, 
discussions of problems, etc.)

APPLICATION, SELECTION ND ADMISSION

To apply, please choose among the registration forms you can find on the 
web-page of the school 
(http://school.diffiety.org/page3/page0/page93/page93.html) the one that 
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).

DEADLINE: Application must be sent not later than Sunday, 21 of June, 2009. 
Applicants will be duly informed by e-mail about their (possible) admission 
- not later than March 16, 2009, if had applied earlier than March 15, 2009; 
- not later than June 21, 2009, if had applied later than March 16, 2009.

REGISTRATION FEE

The registration fee of the school, including a full board (except for 
the meals of the free day) accommodation, amounts to 175 EUR. 
Accompanying persons who want to avail themselves of the school 
accommodation will be requested to pay 150 EUR. Travel expenses are on 
charge of participants.

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 
(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.

ACCOMODATION, MEALS ND 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" 
(http://www.hotelilciliegio.it/pag1.html) is the only high-standard 
lodging solution available in the neighborhoods, located just 
1500 meters away from the center of Santo Stefano del Sole. 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.

FREE DAY

More information about excursion(s) will be duly posted herewith.

ORGANIZING COMMITTE

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

The Organizing Committee can be contacted for any question and suggestion 
via the e-address:

school09it at 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 
attached official poster. 

LOCATION

Santo Stefano del Sole is a small (≈ 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. Exact geographical coordinates are: 
40°54' N, 14°51' E, 510m a.s.l., planet Earth.

Reaching Santo Stefano del Sole is quite easy. The Organizing Committee 
warmly advices the participants not to travel in different dates from the 
official arrival (July 16) and departing (July 31) days, and cannot 
provide travel information for such different dates. Avellino is 263 km 
off Rome and 73 km off Naples, the closest cities reached by 
international flights. A forced stop is the city of Avellino, just 10 
kilometers away from Santo Stefano del Sole. Avellino can be easily 
reached from Rome by bus (there is no direct train connection). More 
information is avalaibla on the web-page of the school 
(http://school.diffiety.org/page3/page0/page93/page93.html).

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--
Sve najbolje, :-)
Marko

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