Athens intensive course Politecnico di Milano November 17 24, 2012

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1 Athens intensive course Politecnico di Milano November 17 24, 2012 Course Title Discrete and Geometric Tomography (POLI8) Professor Responsible Paolo Dulio Saturday, November 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 18 Guided visit of the city the meeting point will be in front of Sant Ambrogio Church at (The church is located in piazza Sant Ambrogio 1. You can reach it by metro with MM2 green line S2Ambrogio metro station) Monday, November 19 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.

2 PIOLA METRO STATION MM2 GREEN LINE DEPARTMENT OF MATHEMATICS IS HERE IN BUILDING B, CALLED NAVE MAIN REFERENCES 1) Richard Gardner, Geometric Tomography, Cambridge University Press, New York, second edition, ) Gabor T. Herman and Attila Kuba Eds., Advances in discrete tomography and its applications, Applied and Numerical Harmonic Analysis. Birkhäuser Boston, Inc., Boston, MA, Further references will be given during the course, and cited papers will be supplied to all interested students.

3 Lectures are given at the Mathematics Department - Seminar Room - 3º Floor Monday, 19 Morning 9:15213:15 PROGRAM 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 X1rays. Continuous and discrete point X1rays. Tuesday, 20 Morning 9:15213:15 Radiographies of lattice sets with discrete parallel X1rays. The reconstruction problem in Discrete Tomography. Description of some algorithms and examples of applications. Switching components. Mid1point construction. U1polygons. Pyramids and related results. Wednesday, 21 Morning 9:15213:15 Uniqueness results by means of radiographies of convex bodies with continuous parallel X1rays. The theorem of Gardner1McMullen in the Euclidean plane. Uniqueness results for classes of lattice sets by means of discrete parallel X1rays. The results of Gardner and Gritzmann in the integer lattice. Thursday, 22 Morning 9:15213:15 Radiographies of convex bodies with point X1rays. The theorem of Volcic in the Euclidean plane. P1polygons. Some results and examples in the lattice. Some remarks about stability of reconstruction. Friday, 23 Morning 9:15212:15 Afternoon 1:0024:00 Exam Correction, marking and discussion Saturday, 24 November Departure

4 Contacts at campus Leonardo Milano Activities Coordinator: Paolo Dulio Tel Politecnico di Milano Dipartimento di Matematica F. Brioschi Piazza Leonardo da Vinci Milano For more information on accommodation and ED activities: Anna Sjöberg Tel /2502 E1mail: Politecnico di Milano Piazza L. Da Vinci 32 I Milano Costs At your arrival you are kindly asked to pay the rest of the amount directly at the hostel and 30 for ED activities to the 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 e1 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 Malpensa Airport: 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:

5 a) Bus to Centrale railway station, 27 daily trips from 8.30 to One1way ticket 6.70 (6.00 if bought at Biglietteria Autostradale in the airport) take b) Bus to Lambrate railway station, 18 daily trips from to One1way ticket 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 h tickets cost 8.25 (unlimited trips) 101ticket carnets (10 one1way ticket 90 ) cost 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

6 MAP of the centre of MILAN mi.it/en/viaggiaconnoi/documents/mappacentromilano.pdf 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. CHECK!!!! Italian Ministry of the Foreign Affairs: