Counting groups, manifolds and primes

Group Actions and Dynamics
Event time: 
Monday, September 16, 2019 - 4:15pm
Alex Lubotzky
Speaker affiliation: 
Hebrew University, Jerusalem/Yale
Event description: 
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.