Speaker: **Yosuke Kubota** (Riken)

Title: Reconstruction of the Bost-Connes groupoid from K-theoretic data

Time/Date: 4:45-6:15, Monday, April 10, 2017.

Room: 118

Abstract:
The Bost-Connes system is a C^{*}-dynamical system (or often said
to be a quantum statistical mechanics) attached to a number field, which
realizes the arithmetics of the number field through its dynamics. It is
first defined by Bost-Connes for the rational number field and
generalized for an arbitrary number field after 15-year effort by many
mathematicians. For the definition, one starts with a groupoid and
consider a restriction of the "dual action" on its convolution
C^{*}-algebra. In this talk, we show that the Bost-Connes groupoids attached
to two number fields are isomorphic if and only if their convolution
C^{*}-algebra have the same K-theoretic data. For the proof, we directly
reconstruct the groupoid from their K-groups. This is a joint work with
Takuya Takeishi.