CIMPA-UNESCO-LEBANON Summer school Algebraic Geometry and Arithmetic of Curves Center for Advanced Mathematical Sciences (CAMS) American University of Beirut (AUB) July 5-16, 2004 ********** ALL ACTIVITIES FOR THE SCHOOL WILL BE HELD ON THE CAMPUS OF THE AMERICAN UNIVERSITY OF BEIRUT, COLLEGE HALL, ROOM B1. ENTER AUB FROM THE MAIN GATE ON BLISS STREET, CLOSE TO JEANNE D'ARC STREET. COLLEGE HALL IS THE BUILDING WITH A CLOCK JUST AHEAD. ENTER COLLEGE HALL BY THE DOOR UNDER THE ARCH. ROOM B1 IS IN THE BASEMENT; GO DOWN ONE FLIGHT OF STAIRS OR TAKE THE ELEVATOR TO LEVEL B1. FOR PARTICIPANTS COMING BY CAR: AUB CANNOT PROVIDE PARKING. PLEASE PARK IN A PARKING LOT ON JEANNE D'ARC STREET OR HAMRA STREET. REGISTRATION FOR THE SCHOOL IS AT 8:00AM-8:30AM IN COLLEGE HALL B1. THE OPENING CEREMONY STARTS AT 8:30AM. ********** Schedule as of July 5 (check school bulletin board for changes) -------------------- Week 1 (July 5-9): +----------+----------+----------+----------+----------+ | M | T | W | Th | F | +----------+----------+----------+----------+----------+ | 8-8:30 | | | | | |register | | | | | +----------+----------+----------+----------+----------+ | 8:30-9:30| 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | | opening | Oesterle | Oesterle | Oesterle | Oesterle | +----------+ | | | | | coffee | | | | | | break +----------+----------+----------+----------+ +----------+ MORNING COFFEE BREAK | | 10-11 | | | Houzel +----------+----------+----------+----------+ +----------+ 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | | 11:05- | Houzel | Houzel | ******* | ***** | | 12:05 | | | Makdisi | Merel | | Oesterle | | | ******* | ***** | +----------+----------+----------+----------+----------+ | | | LUNCH BREAK | | | +----------+----------+----------+----------+----------+ | 2:30-3:30| 2:30-3:30| 2:30-3:30| 2:30-3:30| FRIDAY | | Elzein | Elzein | Elzein | Houzel | AFTERNOON| +----------+----------+----------+----------+ IS | | AFTERNOON COFFEE BREAK | OFF | +----------+----------+----------+----------+ | | 4-5 | 4-5 | 4-5 | 4-5 | | | Jambu | Jambu | Jambu | TBA | | +----------+----------+----------+----------+----------+ Week 2 (July 12-16): +----------+----------+----------+----------+----------+ | M | T | W | Th | F | +----------+----------+----------+----------+----------+ | 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | | Makdisi | Le | Le | Le | Le | +----------+----------+----------+----------+----------+ | MORNING COFFEE BREAK | +----------+----------+----------+----------+----------+ | 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | | Merel | Teissier | Teissier | Teissier | Teissier | +----------+----------+----------+----------+----------+ | LUNCH BREAK | +----------+----------+----------+----------+----------+ | 2:30-3:30| 2:30-3:30| 2:30-3:30| 2:30-3:30| FRIDAY | | Houzel | Makdisi | Makdisi | Makdisi | AFTERNOON| +----------+----------+----------+----------+ IS | | AFTERNOON COFFEE BREAK | OFF | +----------+----------+----------+----------+ | | 4-5 | 4-5 | 4-5 | 4-5 | | | Oesterle | Merel | Merel | Merel | | +----------+----------+----------+----------+----------+ Description of courses: ---------------------- Houzel, Elzein, and Jambu: Riemann surfaces. Analytic theory of curves over C and historical background. Le: Geometry of polynomial functions: Critical points, local monodromy around a critical point, topology of links associated to isolated singularities. Makdisi: Applications of algebraic curves to cryptography, primality testing, and factoring. Merel: Elliptic curves over Q: Mordell-Weil theorem, statement of the fact that every elliptic curve is modular (theorem of Wiles-Breuil-Conrad-Diamond-Taylor) and of its consequences, statement of the Birch-Swinnerton-Dyer conjecture (rank only). Oesterle: Algebraic curves over an arbitrary field. The dictionary between curves and function fields in one variable, differential forms, the genus of a curve, Riemann-Roch theorem, Jacobian of a curve. Teissier: Transcendental study of curves: Singularities of plane curves, Puiseux expansion and topological invariants, and resolution of singularities. ----------------------------------------------------------- For further information, please visit the CAMS website, http://www.cams.aub.edu.lb/ or call the office of CAMS via the AUB main number: (01) 350000 or (01) 374444, extension 4390. CIMPA-UNESCO-LEBANON Summer school Algebraic Geometry and Arithmetic of Curves Center for Advanced Mathematical Sciences (CAMS) American University of Beirut (AUB) July 5-16, 2004 ********** ALL ACTIVITIES FOR THE SCHOOL WILL BE HELD ON THE CAMPUS OF THE AMERICAN UNIVERSITY OF BEIRUT, COLLEGE HALL, ROOM B1. ENTER AUB FROM THE MAIN GATE ON BLISS STREET, CLOSE TO JEANNE D'ARC STREET. COLLEGE HALL IS THE BUILDING WITH A CLOCK JUST AHEAD. ENTER COLLEGE HALL BY THE DOOR UNDER THE ARCH. ROOM B1 IS IN THE BASEMENT; GO DOWN ONE FLIGHT OF STAIRS OR TAKE THE ELEVATOR TO LEVEL B1. FOR PARTICIPANTS COMING BY CAR: AUB CANNOT PROVIDE PARKING. PLEASE PARK IN A PARKING LOT ON JEANNE D'ARC STREET OR HAMRA STREET. REGISTRATION FOR THE SCHOOL IS AT 8:00AM-8:30AM IN COLLEGE HALL B1. THE OPENING CEREMONY STARTS AT 8:30AM. ********** Schedule as of July 6 (check school bulletin board for changes) -------------------- Week 1 (July 5-9): +----------+----------+----------+----------+----------+ | M | T | W | Th | F | +----------+----------+----------+----------+----------+ | 8-8:30 | | | | | |register | | | | | +----------+----------+----------+----------+----------+ | 8:30-9:30| 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | | opening | Oesterle | Oesterle | Oesterle | Oesterle | +----------+ | | | | | coffee | | | | | | break +----------+----------+----------+----------+ +----------+ MORNING COFFEE BREAK | | 10-11 | | | Houzel +----------+----------+----------+----------+ +----------+ 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | | 11:05- | Houzel | Houzel | ******* | ***** | | 12:05 | | | Makdisi | Merel | | Oesterle | | | ******* | ***** | +----------+----------+----------+----------+----------+ | | | LUNCH BREAK | | | +----------+----------+----------+----------+----------+ | 2:30-3:30| 2:30-3:30| 2:30-3:30| 2:30-3:30| FRIDAY | | Elzein | Elzein | Elzein | Houzel | AFTERNOON| +----------+----------+----------+----------+ IS | | AFTERNOON COFFEE BREAK | OFF | +----------+----------+----------+----------+ | | 4-5 | 4-5 | 4-5 | 4-5 | | | Jambu | Jambu | Jambu |**Houzel**| | +----------+----------+----------+----------+----------+ Week 2 (July 12-16): +----------+----------+----------+----------+----------+ | M | T | W | Th | F | +----------+----------+----------+----------+----------+ | 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | 8:30-10 | | Makdisi | Le | Le | Le | Le | +----------+----------+----------+----------+----------+ | MORNING COFFEE BREAK | +----------+----------+----------+----------+----------+ | 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | 10:30-12 | | Merel | Teissier | Teissier | Teissier | Teissier | +----------+----------+----------+----------+----------+ | LUNCH BREAK | +----------+----------+----------+----------+----------+ | 2:30-4***| 2:30-3:30| 2:30-3:30| 2:30-3:30| FRIDAY | | Oesterle | Makdisi | Makdisi | Makdisi | AFTERNOON| +----------+----------+----------+----------+ IS | | AFTERNOON COFFEE BREAK | OFF | +----------+----------+----------+----------+ | | ******** | 4-5 | 4-5 | 4-5 | | | end 4:30 | Merel | Merel | Merel | | +----------+----------+----------+----------+----------+ Description of courses: ---------------------- Houzel, Elzein, and Jambu: Riemann surfaces. Analytic theory of curves over C and historical background. Le: Geometry of polynomial functions: Critical points, local monodromy around a critical point, topology of links associated to isolated singularities. Makdisi: Applications of algebraic curves to cryptography, primality testing, and factoring. Merel: Elliptic curves over Q: Mordell-Weil theorem, statement of the fact that every elliptic curve is modular (theorem of Wiles-Breuil-Conrad-Diamond-Taylor) and of its consequences, statement of the Birch-Swinnerton-Dyer conjecture (rank only). Oesterle: Algebraic curves over an arbitrary field. The dictionary between curves and function fields in one variable, differential forms, the genus of a curve, Riemann-Roch theorem, Jacobian of a curve. Teissier: Transcendental study of curves: Singularities of plane curves, Puiseux expansion and topological invariants, and resolution of singularities. ----------------------------------------------------------- For further information, please visit the CAMS website, http://www.cams.aub.edu.lb/ or call the office of CAMS via the AUB main number: (01) 350000 or (01) 374444, extension 4390.