Monday, September 16, 2019 - 4:15pm
Hebrew University, Jerusalem/Yale
We will report on a series of works in the last 2 decades aroound the following question: “For a given simple Lie group G, how many lattices (i.e., discrete subgroups of finite covolume) does it have of covolume at most x?” Equivalently: “How many manifolds (of volume at most x) are covered by the associated symmetric space.?”As many of these lattices are arithmetic, these questions often lead to deep number theoretic problems: counting primes etc. A recent joint work (joint with M. Belolipetsky) gives a sharp estimate for the number of non unoform lattices in high rank simple groups.