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Seminar

RAS - Research Seminar (Part 1): Random and arithmetic discrete subsets of locally compact groups December 14, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Tobias Hartnick (Technion---Israel Institute of Technology)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Video

Random And Arithmetic Discrete Subsets Of Locally Compact Groups

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

Abstract:

Arithmetic and S-arithmetic groups are important examples of discrete subgroups of locally compact (lc) groups. In this survey talk I will try to convince you that it is their discreteness, rather than their group structure, which makes them interesting. To this end I will explain how large parts of the theory of discrete subgroups of lc groups carries over to non-group subsets of Lie groups, as long as they are "sufficiently discrete”. In fact, it often turns out a posteriori that they have an almost group-like structure. I will illustrate this principle by recent arithmeticity theorems of Machado and Hrushovsky. As in the group case, there is a strong connection between arithmeticity (or super-rigidity) for discrete subsets of groups and certain "random discrete subsets”. This is closely related to the theory of approximate lattices due to Michael Björklund and the speaker.

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Random And Arithmetic Discrete Subsets Of Locally Compact Groups

H.264 Video 25319_28877_8684_Random_and_Arithmetic_Discrete_Subsets_of_Locally_Compact_Groups.mp4