11-Diffiety-poster_thumb XI Edition of the Italian Summer School.
Santo Stefano del Sole (Avellino), Italy.
July 17 - August 1, 2008.
This page was originally posted on February 22, 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



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

Courses

In this edition of the School, the standard courses for beginners will be proposed.
The general classification of Diffiety School's courses is as follows (look at past editions for more information about such courses):

B-COURSE(S): courses for beginners;
A-COURSE(S): advanced courses;
C-COURSE(S): courses for veteran participants.

09:00-10:50 B1 (A. Vinogradov) C (L. Vitagliano)
10:50-11:10 COFFEE BREAK
11:10-13:00 B2 (G. Moreno) A (A. Vinogradov)


Course B1.
Title: Observability in Physics and Differential Calculus over Commutative Algebras.
Lecturer: Prof. Alexandre M. Vinogradov.
Schedule: 1h50' per day (from 09:00 to 10:50).

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: Dr. Giovanni Moreno.
Schedule: 1h50' per day (from 11:10 to 13:00).

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: Prof. Alexandre M. Vinogradov.
Schedule: 1h50' per day (from 11:10 to 13:00).

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: Dr. Luca Vitagliano.
Schedule: 1h50' per day (from 09:00 to 10:50).

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.

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

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.

DEADLINE: Sunday, June 15.

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

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. 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.
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 (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

This list will be populated with the names of the admitted participants as soon as they are successfully selected.
Admitted participants are listed below accordingly to the time of their application. Such a list is regularly refreshed (last update: July 3, 2008).

  1. Jet Nestruev (Moscow, RUSSIA and Salerno, ITALY);
    Elizaveta Gennadievna
    Vishnyakova (Tver', RUSSIA) - Tver State University;
  2. Reza Aghayan (Tehran, IRAN) - Iran University of Science and Technology;
  3. Sevdzhan Hakkaev (Shumen, BULGARIA);
  4. Stanislav Dubrovskiy (Be'er Sheva, ISRAEL) - Ben Gurion University;
  5. Antonio Nigro (Turin, ITALY) - Politecnico Di Torino;
  6. Fereydoon Taheri (Tehran, IRAN) - Sharif University of Technology;
  7. prof. Olga Veniaminovna Kunakovskaya (Voronezh, RUSSIA) - Voronezh State University;
  8. Svetlana Azarina (Voronezh, RUSSIA) - Voronezh State Technical University;
  9. prof. Viacheslav Stepanovich Kalnitskiy (St. Petersburg, RUSSIA) - St. Petersburg State University;
  10. Egor Valerevich Zarubin (St. Petersburg, RUSSIA) - St. Petersburg State University;
  11. Boris Olegovich Zhilko (Karaganda, KAZAKHSTAN) - St. Petersburg State University;
  12. Jenny Santoso (Stuttgart, GERMANY) - University of Stuttgart;
  13. Alexander Zotikov (St. Petersburg, RUSSIA) - SPbGU;
  14. Ildar Sharafutdinov (Ufa, RUSSIA) - St. Petersburg State University;
  15. prof. Tadeusz Jagodzinski (Warsaw, POLAND) - Mathematics and Information Techniques Faculty;
  16. Renat Raisovich Mukhamadiev (Ufa, RUSSIA) - St. Petersburg State University;
  17. Galina Shchekotova (Ekaterinburg, RUSSIA) - St. Petersburg State University;
  18. Stephan W. Anzengruber (Linz, AUSTRIA) - Research Institute for Computational and Applied Mathematics (RICAM);
  19. Farnaz Farzi (Tehran, IRAN) - Khaje Nasir Toosi University of Technology;
  20. Thomas Leuther (Aubel, BELGIUM) - University of Liege;
  21. Victor Erikovich Kasatkin (St. Petersburg, RUSSIA) - St. Petersburg State University;
  22. Zain Ulabidin Shaikh (Aberdeen, UK) - University of Aberdeen;
  23. Joanna Bryk (Płock, POLAND) - Warsaw University of Technology;
  24. Vladimir Suvorov (St. Petersburg, RUSSIA) - St. Petersburg State University;
  25. prof. Alexander Florinsky (St. Petersburg, RUSSIA) - St. Petersburg State University;
  26. prof. Wiesław Sasin (Warsaw, POLAND) - Warsaw University of Technology;

Accommodation, 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 diplomas 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 posted herewith.
24px-Feature_suburban_buses.svg 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. Bächtold, C. Di Pietro, V. Fiore, V. Kalnitsky, M. Langastro, G. Moreno, 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 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.

Location

LogoSantoStefano 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. Section "Pictures" of the X Edition of Summer Diffiety School displays many shots of the School location.
Exact geographical coordinates are: 40°54' N, 14°51' E, 510m a.s.l., planet Earth.
Reaching Santo Stefano del Sole is quite easy.
Foreign participants are kindly suggested to print and/or save an electronic copy of this section and to keep it for the whole duration of their stay in Italy.
The
Organizing Committee warmly advices the participants not to travel in different dates from the official arrival (July 17) and departing (August 1) days, and cannot provide travel information for such different dates.

HowToReachSanto1

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)


24px-Feature_suburban_buses.svg Buses connecting Rome to Avellino on July 17, 2008, are the following:
  • operated by AIR: departures at 16:00 and 20:30 (duration 2:25), from bus station "Autostazione Tiburtina", arrival at bus station "Piazza Kennedy";
  • operated by Marozzi V.T.: departures at 14:40 and 16:00 (duration 3:20), from bus station "Autostazione Tiburtina", arrival at bus station "Piazza Kennedy";
  • operated by Marozzi V.T.: departures at 15:30 (duration 3:10) and 23:59 (duration 2:46), from bus station "Autostazione Tiburtina", arrival at bus station "Avellino Ovest".
24px-Feature_suburban_buses.svg Buses connecting Avellino to Rome on August 1, 2008, are the following:
  • operated by AIR: departures at 06:30 and 14:00 (duration 2:55) from bus station "Piazza Kennedy", arrival at bus station "Autostazione Tiburtina" ;
  • operated by Marozzi V.T.: departures at 06:30 and 07:20 (duration 3:20), from bus station "Piazza Kennedy", arrival at bus station "Autostazione Tiburtina";
  • operated by Marozzi V.T.: departures at 03:45 (duration 2:45) and 11:45 (duration 3:00), from bus station "Avellino Ovest", arrival at bus station "Autostazione Tiburtina".


Bus station "Autostazione Tiburtina" is ≈ 100 meters off the metro station "Tiburtina", in "Via Guido Mazzoni" (look at the map).
Operator Marozzi V.T. sells tickets both online and through the ticket office "Ticket Bus" which is located in "Largo Guido Mazzoni" (look at the map), next to the bus station. Tickets can be booked by calling the free (from Italy) number 899104901.
Operator AIR sells tickets only through the ticket office "Agenzia Piccarozzi" (tel. +39 06 66623140) which is located in "Via Guido Mazzoni" 12/14 (look at the map), next to the bus station. No booking service is provided.

Bus station "Piazza Kennedy" is located next to "Via Carlo Del Balzo" (look at the map).
Tickets for Marozzi V.T. buses are sold by ticket office "D'Ascoli Tours" (tel. +39 0825 26309), located in "Via Tuoro Cappuccini" 13 (look at the map), ≈ 330 meters off the bus station.
Ticket offices selling tickets for AIR buses are located nearby the bus station, either in "Via Circumvallazione" 9 or in "Via Carlo Del Balzo" (look at the map).

40px-Metropolitana_di_Roma.svg Bus station "Autostazione Tiburtina" can be reached by the line "B" of the Roman subway, leaving from the main train station of the capital, "Roma Termini", towards destination "Rebibbia". Line B works from 05:30 to 23:30 (01:30 on Fridays and Saturdays). Single-ride ticket costs 1 euro.

images Airport "Leonardo da Vinci" (FCO), located in "Fiumicino" (34 km off Rome center), is easily connected to train station "Roma Termini" by a special non-stop train called "Leonardo", leaving every 30 minutes from 06:36 to 23:36. One ride takes 31 minutes and one ticket costs 11 euros. Trains from "Roma Termini" to "Leonardo da Vinci" leaves from 05:52 to 22:52.

images Airport "Ciampino" (CIA) (15 km off Rome center) is connected to train station "Roma Termini" by special shuttles cooperating with the airline operators.

24px-Feature_suburban_buses.svg All buses connecting Avellino to Santo Stefano del Sole leaves from bus station "Piazza Kennedy" and are operated by AIR. Bus station "Avellino Ovest" is ≈ 6 km away from bus station "Piazza Kennedy" (look at the map).
Buses connecting Avellino to Santo Stefano del Sole on July 17, 2008, are the following:
07:50 -> 08:15
10:10 -> 10:40
11:10 -> 11:40
12:10 -> 12:45
13:10 -> 13:43
14:30 -> 15:00
16:00 -> 16:30
17:30 -> 18:00
18:30 -> 19:00
20:00 -> 20:30.
Buses connecting Santo Stefano del Sole to Avellino on August 1, 2008, are the following:
06:32 -> 07:00
07:22 -> 07:55
08:15 -> 08:50
09:27 -> 10:00
11:22 -> 11:55
12:22 -> 12:55
13:22 -> 13:55
15:22 -> 15:55
17:12 -> 17:45
18:42 -> 19:15.
Bus stop in Santo Stefano del Sole is located on the intersection of "Via Casa Nigro" and "Via Colacurcio" (look at the map). Tickets are sold by the tobacco shop nearby.

images Airport "Capodichino" (NAP) (6 km off Naples center) is connected to Naples' main bus station "Piazza Garibaldi" by non-stop buses leaving every 20-30 minutes. The airport is also connected directly to Avellino through buses operated by AIR. The bus stop for such a connection is located ≈ 300 meters off Terminal 1.

stazione There are many train connections between Rome and Naples (check the online timetable). Naples main station is called "Napoli Centrale" and is connected to the bus station "Piazza Garibaldi". From "Piazza Garibaldi" leave many AIR buses to Avellino.

24px-Feature_suburban_buses.svg Buses connecting Naples Airport to Avellino on July 17, 2008, are the following:
05:50 -> 06:45
06:25 -> 07:25
06:55 -> 07:55
07:20 -> 08:20
07:40 -> 08:40
08:10 -> 09:10
09:10 -> 10:10
10:10 -> 11:10
11:10 -> 12:10
12:10 -> 13:10
13:10 -> 14:10
13:40 -> 14:40
14:10 -> 15:10
14:40 -> 15:30
15:10 -> 16:10
15:40 -> 16:40
16:10 -> 17:10
16:40 -> 17:40
17:10 -> 18:10
17:40 -> 18:40
18:10 -> 19:10
18:40 -> 19:40
19:10 -> 20:10
19:50 -> 20:50
20:10 -> 21:10
20:40 -> 21:40
21:10 -> 22:00
21:50 -> 22:50
22:40 -> 23:40
23:40 -> 00:40.
24px-Feature_suburban_buses.svg Buses connecting Avellino to Naples Airport on August 1, 2008, are the following:
04:20 -> 05:20
04:50 -> 05:50
05:30 -> 06:30
06:00 -> 07:00
06:40 -> 07:40
07:00 -> 08:00
07:10 -> 08:10
07:50 -> 08:50
08:00 -> 09:00
08:10 -> 09:10
08:50 -> 09:50
09:00 -> 10:00
10:00 -> 11:00
11:00 -> 12:00
12:00 -> 13:00
13:00 -> 14:00
14:00 -> 15:00
15:00 -> 16:00
16:00 -> 17:00
16:59 -> 17:59
17:00 -> 18:00
18:00 -> 19:00
19:00 -> 20:00.
24px-Feature_suburban_buses.svg Buses connecting Naples to Avellino on July 17, 2008, are the following:
05:40 -> 06:45
06:15 -> 07:25
06:45 -> 07:55
07:10 -> 08:20
07:30 -> 08:40
07:45 -> 08:55
08:00 -> 09:10
08:20 -> 09:30
08:40 -> 09:50
09:00 -> 10:10
09:20 -> 10:30
09:40 -> 10:50
10:00 -> 11:10
10:20 -> 11:30
10:40 -> 11:50
11:00 -> 12:10
11:20 -> 12:30
11:40 -> 12:50
12:00 -> 13:10
12:20 -> 13:30
12:40 -> 13:50
13:00 -> 14:10
13:15 -> 14:25
13:30 -> 14:40
13:45 -> 14:55
14:00 -> 15:10
14:15 -> 15:25
14:30 -> 15:30
14:45 -> 15:55
15:00 -> 16:10
15:30 -> 16:40
15:45 -> 16:55
16:00 -> 17:10
16:15 -> 17:25
16:30 -> 17:40
16:45 -> 17:55
17:00 -> 18:10
17:15 -> 18:25
17:30 -> 18:40
17:45 -> 18:55
18:00 -> 19:10
18:15 -> 19:25
18:30 -> 19:40
18:45 -> 19:55
19:00 -> 20:10
19:40 -> 20:50
20:00 -> 21:10
20:30 -> 21:40
21:00 -> 22:00
21:40 -> 22:50
22:30 -> 23:40
23:30 -> 00:40
24px-Feature_suburban_buses.svg Buses connecting Avellino to Naples on August 1, 2008, are the following:
04:20 -> 05:30
04:50 -> 06:00
05:30 -> 06:40
06:00 -> 07:10
06:20 -> 07:30
06:30 -> 07:40
06:40 -> 07:50
06:50 -> 08:00
07:00 -> 08:10
07:10 -> 08:20
07:20 -> 08:30
07:30 -> 08:40
07:40 -> 08:50
07:50 -> 09:00
07:55 -> 09:05
08:00 -> 09:10
08:10 -> 09:20
08:20 -> 09:30
08:30 -> 09:40
08:40 -> 09:50
08:50 -> 10:00
09:00 -> 10:10
09:20 -> 10:30
09:40 -> 10:50
10:00 -> 11:10
10:20 -> 11:30
10:40 -> 11:50
11:00 -> 12:10
11:30 -> 12:40
12:00 -> 13:10
12:30 -> 13:40
13:00 -> 14:10
13:20 -> 14:30
13:40 -> 14:50
14:00 -> 15:10
14:20 -> 15:30
14:30 -> 15:40
14:40 -> 15:50
15:00 -> 16:10
15:20 -> 16:30
15:40 -> 16:50
16:00 -> 17:10
16:20 -> 17:30
16:40 -> 17:50
16:59 -> 18:09
17:00 -> 18:10
17:20 -> 18:30
17:40 -> 18:50
18:00 -> 19:10
18:10 -> 19:20
18:30 -> 19:40
19:00 -> 20:10
19:45 -> 20:55
20:30 -> 21:40
21:15 -> 22:25
22:00 -> 23:10

images-1 In case of need, call taxi services (Avellino tel. 0825 24344, 0825 24444, Salerno tel. 089 757575, Naples tel. 081 5707070, Rome tel. 06 3570). Rates are about 0.8 euro/km.

limousine Santo Stefano del Sole can also be reached by car through highway E841 (connecting Avellino with Salerno), ≈ 6 km after taking "Serino" exit (look at the map).


Piazza del Sole Upon their arrival in Santo Stefano del Sole, participants are kindly requested to present themselves at the registration desk, to be welcomed by the Organizing Committee. Registration desk will be open from 10:30 to 13:30 in the morning, from 15:00 to 21:30 in the evening and from 22:30 to 23:00 in the night of the arrival day (Thursday, July 17). Participants will be asked for registration fee, and given the designated accommodation. Registration desk is located on the ground floor of the Ente Morale "San Vito Martire", which can be found in "Piazza del Sole", between "Via Vito Vingo" and "Via Colacurcio" (look at the map).