EVENT DETAILS AND ABSTRACT

Title: Subshifts and invariant measures under non-standard constraints
Speaker: Van Cyr
Speaker Info:
Brief Description:
Special Note: Chicago Action Now
Abstract:

The Krylov-Bogolyubov says that every topological Z-system has a measure invariant under the dynamics. But what if we seek a measure invariant with additional properties? In this talk I will survey some recent research joint with Kra-Petite and Kra-Schmieding that investigates this question. One sort of measure we seek is a so-called characteristic measure that is invariant under not only the dynamics but also all symmetries of the system. This leads to a definition of a new type of subshift called a locally sofic shift. Another question we investigate is the interaction between non-atomic measures and topological constraints in a certain type of subshift, which we call Furstenberg systems. Throughout, the interplay between topological properties of the subshift and its collection of invariant measures will play a central role.