Ramanujan cubical complexes and non-residually finite groups in dimensions three and higher

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• Alina Vdovina (Newcastle University)
• Friday 07 February 2020, 13:45-14:45
• CMS, MR13.

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Ramanujan graphs were first considered by Margulis and Lubotzky, Phillips, Sarnak to get graphs with optimal spectral properties. In our days the theory of expander graphs and, in particular, Ramanujan graphs is well developed, but the questions is what is the best definition of a higher-dimensional expander is still wide open. There are several approaches, suggested by Gromov, Lubotzky, Alon and others, but the cubical complexes were not much investigated from this point of view.

In this talk I will give new explicit examples of cubical Ramanujan complexes, discuss possible developments and show how to get non-residually finite groups from Ramanujan complexes.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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