Joint Operator algebra and GAMP seminar

Speaker:  Tatiana Smirnova-Nagnibeda (Université de Genève).

Title: Spectra of Laplacians for groups of intermediate growth and their actions".

Abstract: We will discuss a recently discovered connection between the spectral theory of Schrödinger operators whose potentials exhibit aperiodic order, and that of Laplacians associated with certain interesting group actions, as, for example, the action of Grigorchuk's group of intermediate growth on the boundary of the infinite binary tree (based on a joint work with R. Grigorchuk and D. Lenz). The connection goes through a subshift associated with the action; in many cases it is given by a substitution over a finite alphabet that defines the group algebraically, via a recursive presentation by generators and relators. These results can be further used to study the spectra of laplacians on Cayley graphs.