Operator algebra seminar

Speaker: Elizabeth Gillaspy (University of Muenster)

Title: Wavelets and spectral triples for higher-rank graphs

Abstract: In joint work with Farsi, Kang, and Packer, we have constructed a representation of a higher-rank graph C*-algebra C*($\Lambda$) on $L^2(\Lambda^{\infty}, M)$, where $\Lambda^{\infty}$ is the space of infinite paths in the higher-rank graph $\Lambda$ and $M$ is a canonical Borel measure on $\Lambda^{\infty}$. This representation gives rise to a wavelet-type decomposition of $L^2(\Lambda^{\infty}, M)$; in joint work with Farsi, Kang, Julien, and Packer, we have discovered that this wavelet-type decomposition is closely related to the spectral triples and Dirac operators on $\Lambda^{\infty}$ studied by Pearson and Bellissard and by Julien and Savinien.