On spectra of Koopman, groupoid and quasi-regular representations, and spectra of Cayley graphs of some groups of intermediate growth(Rostislav Grigorchuk, Texas A&M)

28.03.2017 10:30

With a countable group G acting on a measure space (X,\mu) one can associate Koopman, groupoid and a family of quasi-regular (permutational) representations on the orbits of the points of the space. All these three types of representations are usually very different from each other. At the same time there is a close relation of the spectra of the Hecke type operators associated with these representations.

In the first part of the talk I will discuss a theorem having roots in my 2000 paper with Laurent Bartholdi/ In the second part I will explain how these ideas can be used to compute the spectrum of the Cayley graph of certain groups of intermediate growth. No knowledge of unitary representations is required. The talk will be based on joint results with Artem Dudko.

Lieu

Room 623, Séminaire "Groupes et Géométrie"

entrée libre