Abstract:The main goal of this course will be to analyze the structure of orbits of polynomial transformations of the affine space of dimension m, with a focus on invertible maps. A large array of techniques is now available, coming from basic Diophantine geometry, p-adic analysis, dynamical or arithmetic equidistribution theorem. I will focus on a small number of precise results that illustra...
AbstractDispersionless integrable hierarchies are obtained as certain limits of classical integrable hierarchies such as the KP hierarchy and the Toda lattice hierarchy. They were introduced in 1990's and studied first, for example, in relation to string theory. In this century it was found that dispersionless hierarchies are closely related to the theory of conformal mappings. I shall talk abo...