Speaker: Zheng Kuang
Title: Constructing groups from prescribed tiles
I will present a method of constructing groups generated by $\omega$-deterministic automata from tiles with given orbits of boundary points. The resulting groups will act on the space of infinite paths of some Bratteli diagrams, which is a generalization of groups generated by bounded automata acting on regular rooted trees. Examples (rather than the general theory) will be provided throughout the talk.
Speaker: Cosmas Kravaris
Title: “Kesten’s Criterion of Amenability”
We provide several equivalent definitions for the amenability of a finitely generated group (without proof). For this talk, we will only need Folner’s criterion of amenability. We prove this is equivalent to Kesten’s criterion of amenability and we discuss its relations with spectral theory and random walks on Cayley graphs.
Speaker: Josiah Owens
Title: Defining Hyperbolic Groupoids
This talk merely aims to define the concept of hyperbolic groupoids. To get there, I'll need to provide some necessary background concerning topological groupoids, pseudogroups and groupoids of germs, compactly generated groupoids and their Cayley graphs, and Gromov hyperbolicity. Along the way, I'll provide some motivational remarks regarding the study of these objects and as many examples as I can fit.
Speaker: Alex Frei
Title: Reduced quotients and the state space on group algebras
We will first study reduced quotients in general.
With this picture in mind, we will then explore how the state space of group algebras relates (one-to-one) to positive definite functions.
We will then explore a particular example of states arising in nature (other than the canonical trace :))
and discuss some of the advantages and disadvantages of positive definite functions.