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Research Talk: Large Scale Geometry of Hecke Pairs

Metric Geometry and Geometric Analysis (Oxford, United Kingdom) July 11, 2022 - July 22, 2022

July 21, 2022 (01:00 PM PDT - 02:00 PM PDT)
Speaker(s): Clément Dell'Aiera (Université de Metz)
Video

Large Scale Geometry Of Hecke Pairs

Abstract

In this talk, we study almost normal subgroups from a geometric point of view. When a group G is equipped with a proper left invariant length, we characterize the subgroups H whose coset space G/H, with the induced metric, is a locally finite space coarsely embeddable into a Hilbert space. We will give examples that i find interesting : these are S-arithmetic groups with quite exotic properties. If time allows, we will present the main application : if H and G/H admit a coarse embeding into a Hilbert space, then G satisfies the Novikov conjecture. 

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Large Scale Geometry Of Hecke Pairs

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