Adrien Douady was an extraordinarily inventive mathematician, and his
work has had enormous influence on many fields of mathematics.
In his thesis, he developed the theory of Banach analytic spaces. This was done under the direction of Henri Cartan and was published in 1966. During the same year, he was invited to speak at the ICM at the age of 31. About 10 years later, he proved the existence of a local moduli space for an arbitrary compact analytic space, solving an important open problem. He published the complete solution in 1974.
Since 1980, his interests shifted to a vast domain called holomorphic dynamics: iterating holomorphic maps, studying their Julia sets and the Mandelbrot set. He is at the origin of the conjecture that the Mandelbrot set is locally connected. He developed the notions of polynomial-like maps, quasiconformal surgery, and parabolic implosion with his student John H. Hubbard. He is at the source of the proof by his students, Xavier Buff and Arnaud Chéritat, of the existence of polynomials having a Julia set of positive area.
Adrien was famous for providing counterexamples on request. He also spread mathematical idea far and wide. A converstation with him was always a pleasure. He had a remarkable ability to make mathematical ideas transparent to many audiences: his book Algèbre et théories galoisiennes, written with Régine, is one example, his film La dynamique du lapin produced with François Tisseyre and Dan Sorensen, is another. The exposition A fractal world, also, produced with Tisseyre, has travelled around the world.
This conference is dedicated to those fields most strongly marked by Adrien's work: complex analytic geometry and holomorphic dynamics. Many of the talks will focus on Adrien's influence on these subjects as well as some of the more recent results.
One evening will be devoted to more personal talks from relatives, friends, and collaborators.
There will also be one evening at the École Normale Supérieure. The Department of Mathematics and Applications will offer a buffet dinner, and a concert in room Dussane: music was an essential component of Adrien's life.
