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4:00 pm Thursday, November 15, 2012 Colloquium: Compact quotients of reductive homogeneous spaces: geometric and spectral aspectsby Fanny Kassel (Université Lille) in HB 227- I will discuss the so-called "problem of compact quotients": given a homogeneous space G/H, are there discrete subgroups Gamma of G acting properly discontinuously on G/H with a compact quotient? In other words, are there compact manifolds that are locally modeled on G/H and complete? If G/H is a Riemannian symmetric space, the answer is yes by work of Borel and Harish-Chandra. If G/H is non-Riemannian (for instance SO(p+1,q)/SO(p,q) with pq nonzero), the answer may be no, and it is conjecturally yes only in some geometrically meaningful examples. I will describe some of these examples, focussing in particular on the Lorentzian analogues of hyperbolic 3-manifolds. Finally, I will discuss the spectral properties of the Laplacian on non-Riemannian symmetric spaces.
Submitted by jtanis@rice.edu |