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Ergodic Theory/Probability Seminar - Elliot Paquette

Elliot Paquette
September 14, 2017
3:00PM - 4:00PM
Math Tower 154

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Add to Calendar 2017-09-14 15:00:00 2017-09-14 16:00:00 Ergodic Theory/Probability Seminar - Elliot Paquette Title: Distributional Lattices in Symmetric spaces.Speaker: Elliot Paquette (Ohio State University)Abstract: A Riemannian symmetric space X is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. A lattice in such a space can be considered as a discrete subgroup G of isometries so that a Borel fundamental domain of the quotient space G/X has finite Riemannian volume. Lattices mirror the structure of the ambient space in many ways: for example, X is amenable if and only if the the ambient space is amenable. We introduce the notion of a distributional lattice, generalizing the notion of lattice, by considering measures on discrete subsets of X having finite Voronoi cells and certain distributional invariance properties. Non-lattice distributional lattices exist in any Riemannian symmetric space: the Voronoi tessellation of a stationary Poisson point process is an example. With an appropriate notion of amenability, the amenability of a distributional lattice is equivalent to the amenability of the ambient space. We give some open problems related to these processes and some pretty pictures. Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: Distributional Lattices in Symmetric spaces.

SpeakerElliot Paquette (Ohio State University)

Abstract: A Riemannian symmetric space X is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. A lattice in such a space can be considered as a discrete subgroup G of isometries so that a Borel fundamental domain of the quotient space G/X has finite Riemannian volume. Lattices mirror the structure of the ambient space in many ways: for example, X is amenable if and only if the the ambient space is amenable. We introduce the notion of a distributional lattice, generalizing the notion of lattice, by considering measures on discrete subsets of X having finite Voronoi cells and certain distributional invariance properties. Non-lattice distributional lattices exist in any Riemannian symmetric space: the Voronoi tessellation of a stationary Poisson point process is an example. With an appropriate notion of amenability, the amenability of a distributional lattice is equivalent to the amenability of the ambient space. We give some open problems related to these processes and some pretty pictures.

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