# Jerusalem Mathematics Colloquium

Thursday, 22nd October 2009, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Alex Lubotzky

(Hebrew University)

"Counting groups, manifolds and primes"

** Abstract: **

We will report on a series of works in the last decade around
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.

We will concentrate on recent works which give very sharp
results for counting arithmetic lattices in SL(2). Here the
representation theory of the symmetric groups also comes into the game.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2009-10

Archive of talks