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Seminar

RAS - Research Seminar (Part 1): Convergence of locally symmetric spaces November 16, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Jean Raimbault (Université de Toulouse III (Paul Sabatier))
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

Convergence Of Locally Symmetric Spaces

Abstract/Media

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

Abstract: This talk will be motivated by the following conjecture put forth by Tsachik Gelander : for any symmetric space X there exists a constant C such that any arithmetic quotient of X is homotopy equivalent to a simplicial complex with at most C times its volume simplices and where every vertex has degree at most C.

A standard construction gives a positive answer to this question if we assume that there is a lower bound for the injectivity radius of arithmetic X-manifolds. This might be true but seems far out of reach at present, so I will introduce a weaker condition ("quantitative Benjamini--Schramm convergence to X") which still implies it. For 3-dimensional hyperbolic manifolds Mikołaj Frączyk proved that it holds and thus proved the Gelander conjecture for those. I will report on a work in progress with Mikołaj where we extend his argument to other locally symmetric spaces; our current main result being a non-quantitative version of convergence which does not imply the Gelander conjecture.

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Convergence Of Locally Symmetric Spaces

H.264 Video 25315_28873_8632_Convergence_of_Locally_Symmetric_Spaces.mp4