Athens intensive course
Politecnico di Milano
November 12 – 19, 2011
Title of the Course:
Discrete and Geometric Tomography (POLI8)
Professor Responsible:
Paolo Dulio

Saturday, November 12

  • 15.00 - meeting at Hostel La Cordata, via Burigozzo 11, Milan. (nearest metro: MM Missori)
  • During the afternoon – little tour of Milano
  • Welcome drink downtown (happy hour)

Sunday, November 13

  • Guided visit of the city

the meeting point will be in front of Sant’Ambrogio Church at 10.00

(The church is located in piazza Sant’Ambrogio 1. You can reach it by metro with MM2 green line S-Ambrogio metro station)

Monday, November 14

The course will take place at the Department of Mathematics, via Bonardi, Milano (Building NAVE).

We will meet there at the ground floor at 9.00.

MAIN REFERENCES

1)Richard Gardner, Geometric Tomography, Cambridge University Press, New York, second edition, 2006.

2)Gabor T. Herman and Attila Kuba Eds., Advances in discrete tomography and its applications, Applied and Numerical Harmonic Analysis. Birkhäuser Boston, Inc., Boston, MA, 2007.

PROGRAM

Monday, 14 Morning 9:15-13:15 Afternoon 2:30-4:30

SeminarRoom- 3º Floor

A brief history of CAT. Qualitative description of the Radon transform. The origin of Geometric Tomography. Hammer’s problem and related uniqueness problems. Discrete Tomography and related problems. Continuous and discrete parallel X-rays. Continuous and discrete point X-rays. An overview of geometric transformations in the plane. Projective transformations. Cross-ratio for collinear points and for line in a pencil.

Tuesday, 15Morning 9:15-13:15 Afternoon 2:30-4:30

SeminarRoom- 3º Floor

Radiographies of lattice sets with discrete parallel X-rays. The reconstruction problem in Discrete Tomography. Description of some algorithms and examples of applications. Switching components. Mid-point construction. U-polygons. Pyramids and related results.

Wednesday, 16 Morning 9:15-13:15 Afternoon 2:30-4:30

SeminarRoom- 6º Floor

Uniqueness results by means of radiographies of convex bodies with continuous parallel X-rays. The theorem of Gardner-McMullen in the Euclidean plane. Uniqueness results for classes of lattice sets by means of discrete parallel X-rays. The results of Gardner and Gritzmann in the integer lattice.

Thursday, 17 Morning 9:15-13:15 Afternoon 2:30-4:30

SeminarRoom- 3º Floor

Radiographies of convex bodies with point X-rays. The theorem of Volcic in the Euclidean plane. P-polygons. Some results and examples in the lattice. Some remarks about stability of reconstruction.

Friday, 18

SeminarRoom- 3º Floor

Morning 9:15-12:15 Exam

Afternoon 1:00-4:00 Correction, marking and discussion

Around 4:00 p.m. Farewell buffet.

Saturday, 19 November

Departure
Contacts at campus Leonardo Milano
Activities Coordinator: Paolo Dulio
Tel. +39 02 2399 4577 / Politecnico di MilanoDipartimento di Matematica F. BrioschiPiazza Leonardo da Vinci 3220133 Milano
For more information on accommodation and ED activities: Michela Gregori
Tel. +39 02 2399 2523/9733E-mail: / Politecnico di MilanoPiazza L. Da Vinci 32I-20133 Milano

Costs

At your arrival you will have to pay the rest of the amount directly at the hostel.

€ 30 for ED activities - to local coordinator

Please note:

All transports in Milano, transports from/to the airport/railway stations at arrival/departure are not included.

Housing in Milano

Athens students (who requested housing in the application form or by e-mail) have been reserved a booking at

Hostel La Cordata via Burigozzo 11 in Milano.

The hostel is in the very city centre and it is easily reachable:
* From the Central Station (Stazione Centrale):

take Metro line 3 (yellow line), stop in Missori, take Corso Italia and catch tram n. 15 (direction Gratosoglio/Rozzano) for two stops
* From Linate Airport:

take bus n. 73 in Corso Europa/San babila, walk to Piazza Fontana and catch tram n.15 for 4 stops.

* From MalpensaAirport:

a) catch Malpensa Express, get off in Cadorna Station, catch bus n. 94, get off in Molino delle Armi street/ and turn in Santa Croce street.
b) catch Malpensa Shuttle, get off in Central station, take Metro line 3 (yellow line), stop in Missori, take Corso Italia and catch tram n. 15 (direction Gratosoglio/Rozzano) for two stops

From Orio al Serio Airport:

a)Bus to Centrale railway station, 27 daily trips from 8.30 to 01.00. One-way ticket 6.70€ (6.00 € if bought at Biglietteria Autostradale in the airport) – take

b)Bus to Lambrate railway station, 18 daily trips from 05.35 to 23.50. One-way ticket 6.00€. then take the Metro green line to Centrale and then take Metro line 3 (yellow line), stop in Missori, take Corso Italia and catch tram n. 15 (direction Gratosoglio/Rozzano) for two stops

Lunch and evening meals

During you stay at the Politecnico di Milano in Milano, you have to arrange your lunch and evening meals.

Meals are not included in the sum you will pay for social activities (only first Friday night).

For cheap lunches around the campus please check the map below.

The most popular area for student to find nice places to eat at reasonable prices is the Navigli Area. To reach it, the quickest way is to take the metro – green line until P.ta Genova metro station.

Dinner in any place will cost a minimum of 18€ if you have a pizza.

More about transports in Milan

Tariffs for metro and surface transports are the same.

The urban network ticket costs 1.50€ and it is valid for 90’ on all lines (but it cannot be used twice on the metro if you get out of the metro station).

Tickets are sold in newspapers kiosks, bars, tobacconist’s and it cannot be bought on board.

Public transportations run every day from 6.00 to midnight, but some buses provide nocturnal service.

The are also tourist tickets:

24h tickets cost 4.50€

48h tickets cost 8.25€ (unlimited trips)

10-ticket carnets (10 one-way ticket 90’) cost 13.80€

Weekly (2trips90’x6days) 8.40€

We kindly recommend you to buy for the week end the 48h ticket, since it will e easier and less expensive to use it in Milano.

For more information about transports

Health Insurance form

If you are an EU citizen, during your stay, you can benefit from the Italian health care service. You have to provide yourself with the E111 form before your departure.

Student visa

If you are a non EU citizen, you have to provide yourself with a temporary student visa.

Italian Ministry of the Foreign Affairs: