Alex Lubotzky, Weizmann Institute, The Hebrew University, and Minerva Distinguished Visitor High dimensional expanders and Ramanujan complexes Wednesday, Oct 4 Fine Hall Common Room / 12:15 PM – 1:15 PM 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)(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.