Nuclear Dimension of Graph C*-algebras with Condition (K)

• Speaker: Gregory Faurot, University of Nebraska-Lincoln
• Time: 3:10pm to 3:20pm
• Abstract: Nuclear dimension is a useful tool in the classification of C*-Algebras, first described by Winter and Zacharias. Involving finite dimensional approximations and "colorings" of cpc maps of order zero, nuclear dimension is a non-commutative analogue of covering dimension from topology. Nuclear dimension is well understood in the case of simple C*-algebras. Graph algebras are an approachable class of non-simple C*-algebras. In this talk, we give some results about the nuclear dimension of C*(E), when E is a directed graph with Condition (K). This is joint work with Christopher Schafhauser.

Polar decomposition in algebraic K-theory

• Speaker: Pawel Sarkowicz, University of Waterloo
• Time: 3:10pm to 3:20pm
• Abstract: We consider the relationship between the (Hausdorffized) algebraic K_1 group and the (Hausdorffized) unitary algebraic K_1 group. Unlike for topological K-theory, these two groups do not agree in general. However, we discuss how polar decomposition gives a natural relationship between the two, with the caveat that we must keep track of positive invertibles by their tracial behaviour. This is joint with Aaron Tikuisis.