## Monday Analysis Seminar: K-theory for operator algebras and Bass–Serre theory

Date
2015-11-4 16:30 - 2015-11-4 18:00
Place
Faculty of Science Buliding #3 Room 210
Speaker/Organizer
Kei Hasegawa (Kyushu University)

A C*-algebra is a self-adjoint'' algebra of bounded linear operators on a Hilbert space which is closed in the norm topology. In this seminar, I will talk about the problem that, for given C*-algebras A and B, how can we compute the K-theory of their (amalgamated) free products from those of A and B for non-specialists.

In the first half of the seminar, I review the historical background of the problem since 1970s, introducing two concrete C*-algebras: the C*-algebra associated with the free group of rank 2 and the non-commutative tori.

In the second half of the seminar, I talk about K-theory of C*-algebras associated with amalgamated free products of discrete groups. Here, the notion of amenability and Bass--Serre theory play important roles. Finally, I will explain my recent result on K-theory of amalgamated free products of general C*-algebras.

Different time and day of the week.