Alex Lubotzky - From Ramanujan to Gromov
October 25, 2023 - Princeton University
This talk is the third of five lectures in Alex Lubotzky's Fall 2023 Minerva Mini-course, "High Dimensional Expanders and Their Applications in Mathematics and Computer Science"
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.