Alex Lubotzky - High dimensional expanders and Ramanujan complexes
October 4, 2023 - Princeton University
This talk is the second of five lectures in Alex Lubotzky's Fall 2023 Minerva Mini-course, "High Dimensional Expanders and Their Applications in Mathematics and Computer Science"
The seminal work of Howard Garland in the 60's, proving the conjecture of Serre on vanishing cohomology of lattices in p-adic simple Lie groups reveals that high dimensional expanders (HDX) have a ``local to global" phenomenon which does not exist in graphs. Furthermore, the work of L. Lafforgue, generalizing Drinfeld's work from GL(2) to GL(n), called for the construction of Ramanujan complexes. These high dimensional simplicial complexes led to the development of a rich theory with applications in CS and math.