Mario Klisse: Topological boundaries of connected graphs and Coxeter groups
C*-algebra seminar talk by Mario Klisse (Delft)
The talk will be online, via zoom.
Title: Topological boundaries of connected graphs and Coxeter groups
Abstract: In this talk we will present a method which allows to associate certain topological spaces with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and are particularly tractable in the case of Cayley graphs of finite rank Coxeter groups. In that context we speak of the compactification and the boundary of the Coxeter group. They have some desirable properties and nicely relate to various other important constructions such as Gromov's hyperbolic compactification, the Higson compactification and Furstenberg boundaries of Coxeter groups.
The study of (certain) compactifications and boundaries of groups has lots of interesting operator algebraic applications. For instance, they play a role in the rigidity theory of von Neumann algebras and are crucial in Kalantar-Kennedy's solution of the simplicity question for group C*-algebras. Our construction turns out to be closely related to Hecke C*-/ and Hecke von Neumann algebras. These are operator algebras associated with (Iwahori) Hecke algebras. We will discuss some implications of this connection.