School of Mathematics & Physics, University of Lincoln
On the 27th of February 2019, Dr Alina Vdovina (Newcastle University) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk on “Ramanujan cubical complexes as higher-dimensional expanders”.
Abstract: Ramanujan graphs were first considered by 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 and discuss possible developments.