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Status |
Confirmed |
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Seminar Series |
MATH-IHES |
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Subjects |
math |
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Date |
Monday 20 January 2025 |
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Time |
14:00 |
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Institute |
IHES |
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Seminar Room |
Amphithéâtre Léon Motchane |
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Speaker's Last Name |
Parreau |
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Speaker's First Name |
Anne |
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Speaker's Email Address |
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Speaker's Institution |
Université Grenoble Alpes |
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Title |
Hilbert Geometry over Non-Archimedean Ordered Fields |
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Abstract |
I will explain how convex projective geometry over non-Archimedean ordered fields may be used to study large scale properties of individual real Hilbert geometries and degenerations of convex projective actions, using a projective geometry version of ultralimits. Non-Archimedean convex subsets have a naturally associated quotient Hilbert metric space. In the case of ultralimits, we show that it is the ultralimit of the real Hilbert metric spaces under a natural non-degeneracy condition. I will present some examples and give a full description of the Hilbert metric space for non-Archimedean polytopes defined over R, which correspond to the asymptotic cones of a fixed real polytope. This is joint work with Xenia Flamm. |
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arXiv Preprint Number |
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Comments |
Séminaire Géométrie et groupes discrets |
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Attachments |
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