Werner Müller - Microlocal and Global Analysis,...
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Werner Müller - Microlocal and Global Analysis, Interactions with Geometry
Approximation of L2-invariants of locally symmetric space.
L2-invariants are dened in terms of the universal covering of a compact manifold as counterparts of
classical invariants such as Betti numbers, the index of elliptic operators, or the analytic torsion. They have important
applications in topology and geometry. In particular, they are related to the study of the asymptotic behavior of
Betti numbers, analytic torsion and other spectral invariants for sequences of nite coverings converging in the
Benjamini-Schramm sense to the universal covering. In this talk I will consider this problem for locally symmetric
spaces. This is closely related to the limit multiplicity problems of DeGeorge-Wallach, Delorme and others. I will
review some recent results and discuss some open problems.