##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Amanda Wilkens

#### University of Texas, Austin

## Poisson-Voronoi tessellations and fixed price in higher rank

##### Abstract:

We overview the cost of a group action, which measures how much information is needed to generate its induced orbit equivalence relation, and the ideal Poisson-Voronoi tessellation (IPVT), a new random limit with interesting geometric features. In recent work, we use the IPVT to prove all measure preserving and free actions of a higher rank semisimple Lie group on a standard probability space have cost 1, answering Gaboriau's fixed price question for this class of groups. We sketch a proof, which relies on some simple dynamics of the group action and the definition of a Poisson point process. No prior knowledge on cost, IPVTs, or Lie groups will be assumed. This is joint work with Mikolaj Fraczyk and Sam Mellick.

Brandon Seward

### October 3, 2023

### 10:00 AM

APM 7218 and Zoom ID 967 4109 3409

Research Areas

Ergodic Theory and Dynamical Systems****************************