Abstract

The problem of characterizing equivalence classes, under holomorphic changes of coordinate, of holomorphic germs at the origin which are tangent to the identity was solved in the early 1980′s by Ecalle and Voronin (independently). I will discuss the history and motivation for this problem as well as it′s solution (without proof). Then I will discuss an application of the methods of Ecalle and Voronin to the solutions of some geometrical problems that have been recently obtained by myself and X. Gong.