Invited talk

Friday, July 23, 12:15 ~ 13:15 UTC-3

Symbolic systems, automorphism groups, and invariant measures

Bryna Kra

Northwestern University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The automorphism group of a symbolic system capture its symmetries, reflecting the dynamical behavior and the complexity of the system. For example, for a topologically mixing shift of finite type, the automorphism group contains isomorphic copies of all finite groups and the free group on two generators and such behavior is common for shifts of high complexity. In the opposite setting of low complexity, there are numerous restrictions on the automorphism group, and for many classes of shift systems, it is known to be virtually abelian. I will give an overview of relations among dynamical properties of the system, algebraic properties of the automorphism groups, and measurable properties of the system and of its automorphism group, all of which quickly lead to open questions.

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