these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

for some 3 million years, the archaeological record is characterized by stone tools undergoing incremental changes. then around 40,000 years ago, the monotony of lithics is terminated by a profusion of visual representations, generally considered to be the world’s first objets d’art. this collection include a series of portable objects, especially figurines and, later on, the famous cave painti...

This article develops a general theory about how representative systems might best promote democratic legitimacy – one that recognizes the potential benefits of networked responsiveness between diverse kinds but is alert to threat fragmentation and value simplicity. Deliberative constructivist theorists representation tend agree more pluralistic are democratic. I will argue, however, can bias t...