### Nonsingular Poisson suspensions

- Series
- CDSNS Colloquium
- Time
- Friday, February 3, 2023 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Online
- Speaker
- Oleksandr Danilenko – Institute for Low Temperature Physics and Engineering

https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

Let T be an invertible measure preserving transformation of a standard infinite measure space (X,m). Then a Poisson suspension (X*,m*,T*) of the dynamical system (X,m,T) is a well studied object in ergodic theory (especially for the last 20 years). It has physical applications as a model for the ideal gas consisting of countably many non-interacting particles. A natural problem is to develop a nonsingular counterpart of the theory of Poisson suspensions. The following will be enlightened in the talk:

--- description of the m-nonsingular (i.e. preserving the equivalence class of m) transformations T such that T* is m*-nonsingular

---algebraic and topological properties of the group of all m*-nonsingular Poisson suspensions

--- an interplay between dynamical properties of T and T*

--- an example of a "phase transition" in the ergodic properties of T* depending on the scaling of m

--- applications to Kazhdan property (T), stationary (nonsingular) group actions and the Furstenberg entropy.

(joint work with Z. Kosloff and E. Roy)