Aaron Tikuisis, University of Aberdeen
“C*-algebras: quasidiagonality and amenability”
A C*-algebra is a set of bounded operators on a Hilbert space, which is norm-closed and closed under the addition, scalar multiplication, composition, and adjoint operations. They arise naturally through a variety of constructions; for example, we’ll see ways of constructing a C*-algebra from a group, and from a group action on a topological space. An open-ended question in C*-algebra theory concerns what information a C*-algebra retains about the object from which it is constructed. The answer - not just which properties of the input are reflected in the C*-algebra, but also which C*-algebraic property it corresponds to - is often interesting.
Quasidiagonality is a somewhat mysterious property of C*-algebras, arising in 1970 in ideas of Halmos. It has long been known to have some weak connection to concepts of amenability (both the property of groups, and a related C*-algebraic property). I will introduce quasidiagonality and discuss joint work with S. White and W. Winter, in which we established that the connection between qua- sidiagonality and amenability is much deeper than it formerly appeared. Our result has consequences relating to recent major advances in the structure and classification of C*-algebras.
MC 5501
Refreshments will be served in MC 5501 at 3:30 pm. Everyone is welcome to attend.