PIMS Distinguished Lecture Series: Joachim Cuntz

We will first present the algebras A(K) associated with a number field K which were introduced and analyzed in joint work with X.Li. The computation of their K-theory is a challenging problem. It turns out to be determined by the multiplicative group of the field. The requirement of functoriality of the construction leads to a canonical "Toeplitz type"-extension of the algebra A(K) which very closely reflects the structure of the number field K (zeta-function, class number etc.). We will then discuss this new type of algebra in detail.