Title: SL(2,C) character varieties in low-dimensional topology: Connections with number theory and algebraic geometry. Lecturer: Alan Reid, Rice University Abstract: Let G be a finitely generated group. In these lecture we will study the collection R(G) of homomorphisms G---> SL(2,C). This has the structure of an algebraic set. We will also study the associated character variety which arises a certain quotient X(G) of R(G) (essentially by the conjugation action). We will mainly be interested in groups that arise in low-dimensional topology and geometry; e.g. free groups, surface groups and knot groups. There will be many examples and explicit computations. We will discuss these in the context of number theoretic and algebraic questions about components in the character variety.