ERC Advanced Grant

This project is concerned with problems in several areas. A starting point is the new concept of a ring C*-algebra associated with a countable ring without zero divisors. For special rings this C*-algebra has a very rich and surprising structure. A particularly interesting case is the ring of algebraic integers in a global field. In this context the algebra contains well known topological dynamical systems. We plan to use the analysis of ring algebras as an organizing principle for the study of many questions in C*-algebra theory, K-theory, ergodic theory and number theory. Some of these questions are well known and very difficult.