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SUMMARY:Ramanujan cubical complexes and non-residually finite groups in di
 mensions three and higher - Alina Vdovina (Newcastle University)
DTSTART:20200207T134500Z
DTEND:20200207T144500Z
UID:TALK137782@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Ramanujan graphs were first considered by Margulis and Lubotzk
 y\, Phillips\, Sarnak to get graphs with optimal spectral properties. In o
 ur days the theory of expander graphs and\, in particular\, Ramanujan grap
 hs is well developed\, but the questions is what is the best definition of
  a higher-dimensional expander is still wide open. There are several appro
 aches\, suggested by Gromov\, Lubotzky\, Alon and others\, but the cubical
  complexes were not much investigated from this point of view.\n\nIn this 
 talk I will give new explicit examples of cubical Ramanujan complexes\, di
 scuss possible developments and show how to get non-residually finite grou
 ps from Ramanujan complexes.
LOCATION:CMS\, MR13
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