Algebraic Geometry and Arithmetic of Curves

Location

BEIRUT
,
Lebanon

Dates

to

Presentation

This school will present various aspects of the theory of algebraic curves, as a way of introducing students, as well as researchers not specializing in these fields, to the areas of algebraic geometry and arithmetic geometry. A related goal is to assemble a regional network of mathematicians working in algebra, number theory, and algebraic geometry. The school also aims to promote collaboration between mathematicians from the region and research teams in Europe, both on the level of joint research projects and in shared advising (co-advising) of thesis students. The school will help students from the region complete their mathematical training, with the goal of eventually entering a doctoral program, while at the same time making contact with potential thesis advisors or co-advisors.

Administrative and scientific coordinators

Kamal Khuri-Makdisi (American University of Beirut,
Lebanon
,
kmakdisi@aub.edu.lb
)
Fouad Elzein (University of Nantes,
France
,
fouad.elzein@wanadoo.fr
)

Scientific program

Course 1: "Riemann surfaces: Analytic theory of curves over C and historical background", Christian Houzel (Univ. Paris VII, France) & Fouad Elzein (Univ. Nantes, France) & Michel Jambu (Univ. Nantes, France)

Course 2: "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", Joseph Oesterlé (Univ. Paris VI, France)

Course 3: "Geometry of polynomial functions: Critical points, local monodromy around a critical point, topology of links associated to isolated singularities", Dung Trang Lé (ICTP, Trieste, Italy)

Course 4: "Transcendental study of curves: Singularities of plane curves, Puiseux expansion and topological invariants, and resolution of singularities.", Bernard Teissier (CNRS, Univ. Jussieu, France)

Course 5: "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)", Loïc Merel (Univ. Paris VII, France)

Course 6: "Applications of algebraic curves to cryptography, primality testing", Kamal Khuri-Makdisi (American Univ. of Beirut, Lebanon)

Website of the school

http://www.cimpa-icpam.org/anciensite/Anglais/AnciensProg/2004/Lebanon04.html

How to participate