Notice
Point processes on higher rank symmetric spaces and their cost
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Descriptif
Cost is a natural invariant associated to group actions and invariant point processes on symmetric spaces (such as Euclidean space and hyperbolic space). Informally, it measures how difficult it is to "connect up" the point process. In recent joint work with Mikolaj Fraczyk and Amanda Wilkens, we showed that higher rank symmetric spaces have "fixed price one", that is, the cost of any aperiodic invariant point process on such a space is one. By applying a theorem of the author with Miklos Abert (or a theorem of Carderi, independently proved), we get uniform vanishing of rank gradient for sequences of lattices, resolving a conjecture of Abert-Gelander-Nikolov.
The proof makes use of the ideal Poisson Voronoi tessellation (IPVT), a new object first introduced in a beautiful paper of Budzinski, Curien, and Petri. In this talk, I will explain what cost is and how the strange properties of the IPVT in higher rank yield fixed price one.
Thème
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