From Ramanujan to Gromov

Alex Lubotzky, Minerva Distinguished Visitor, & Weizmann Institute
Fine Hall Common Room

In this talk we will show how the Ramanujan complexes lead to solution of the geometric, and then the topological, Gromov overlapping problem. The technical tool is via the notion of ``coboundary expansion". This cohomological concept was developed parallelly and independently by Gromov for overlapping problems and by Linial-Meshulam in order to extend Erdős-Rényi theory of random graphs to higher dimensional simplicial complexes.