Seminar
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| Location: | SLMath: Online/Virtual |
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.
Convergence Of Locally Symmetric Spaces
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.
No Notes/Supplements UploadedConvergence Of Locally Symmetric Spaces
| H.264 Video | 25315_28873_8632_Convergence_of_Locally_Symmetric_Spaces.mp4 |