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LA Probability Forum

Thursday, October 5, 2023
3:00pm to 4:00pm
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Poisson-Voronoi tessellations and fixed price in higher rank
Amanda Wilkins, Department of Mathematics, University of Texas, Austin,

USC, Kaprelian (KAP) 414

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.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].