Abstract A representation of a group G is said to be rigid, if it cannot be continuously deformed to a non-isomorphic representation. If G happens to be the fundamental group of a complex projective manifold, rigid representations are conjectured (by Simpson) to be of geometric origin. In this talk I will outline the basic properties of rigid local systems and discuss several consequences of Si...
Abstract:The ideas of renormalization was introduced into dynamics around 40 years ago. By now renormalization is one of the most powerful tools in the asymptotic analysis of dynamical systems. In this talk I will discuss the main conceptual features of the renormalization approach,and present a selection of recent results. I will also discuss open problems and formulate related conjectures.Sp...