[Binghamton Geometry/Topology Seminar] October 23

[Marco Varisco]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR
  http://www.math.binghamton.edu/dept/topsem/

Date:  Thursday, October 23, 2008

Time:  2:50 pm

Place:  Library North 2205
  (followed by coffee/tea in the Anderson Reading Room)

Speaker:  David Constantine (University of Michigan)

Title:  A result on compact Clifford-Klein forms of SL_{n-2}(R)\SL_n(R)

Abstract:  The problem of Clifford-Klein forms is to determine for
which pairs of Lie groups (H, J), with J a closed subgroup of H, there
is a discrete subgroup ¦£ of H so that the quotient J\H/¦£ is a compact
manifold. Methods from topology, geometry, dynamics, and
representation theory have been used to approach this problem and many
cases are still open. For example, the basic test case of
SL_{n-k}(R)\SL_n(R) is not fully solved ¨C nonexistence has been proved
for k>2 and for k=1 and n odd, but the other cases are open. In this
talk I'll very briefly survey the general problem and then present a
result on compact forms of SL_{n-2}(R)\SL_n(R) which gives an
algebraic characterization of any possible compact form and reduces
the problem to an algebraic one about subgroups of SL_n(R). The proof
relies on techniques from three important parts of rigidity theory for
group actions, cocycle superrigidity, Ratner's theorems for unipotent
flows and measure rigidity.