“The nucleus of the universe, a very small part right at the centre, about 10-35 metres in diameter”, says the mathematician Jean-Pierre Demailly, “could be a Calabi-Yau manifold, which is a special example of Kahler compact manifolds”. These exotic names refer to the complex geometrical structures being studied by Demailly, who will give one of the ICM2006 plenary lectures, during which he will present the latest advances in the understanding of the geometrical structure of Kahler projective algebraic manifolds.

Knowledge of these structures provides potential applications in other fields of mathematics such as algebra or topology. Demailly employs analytical methods, a branch of mathematics, to solve problems in other areas of this science as well as other sciences, since in his methods he includes the solution of the Monge-Ampère equations, which are related to the general theory of relativity equations.

Manifolds are mathematical constructions that generalize the idea of curve and su***ce to any dimension and any body. Professor Demailly’s talk will focus on the study of Kahler manifolds in the field of complex numbers. These manifolds are a generalization of projective algebraic manifolds, which are the solution to a system of polynomial homogeneous equations.

Jean-Pierre Demailly was born in 1957 in Péronne (France). He began his mathematical studies in 1973, and graduated from the University of Paris VII in 1976. Under the supervision of Henri Skoda he wrote his doctoral thesis “On the Different Aspects of Positivity in Complex Analysis” (“Sur differents aspects de la positivité en analse complexe”, which he defended in 1982. He has been professor at the Joseph Fourier University in Grenoble since 1983. In 1994 he was elected a member of the Academy of Sciences, and in 2002 a senior member of the Institut Universitaire de France (IUF). He has gained much recognition and won several awards, the 1996 Humboldt Prize for International Collaboration from the Max Planck Society among them.

Speaker: Jean-Pierre Demailly

Title: “Compact K?hler Manifolds and Transcendental Techniques in Algebraic Geometry”

Date: Tuesday, August 29th. 10:15-11:15    

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