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Colloquium (Mathematische Gesellschaft)
# Higher Kazhdan projections, K-theory and applications to delocalised L^2 Betti numbers

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SZ (MI)
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#### MI

Description

For a discrete group G, higher Kazhdan projections are projections constructed from the reduced cohomology of G with coefficients in unitary representations. If a unitary representation has spectral gap, then such projections lie in the group C*-algebra associated with the unitary representation and give rise to K-theory elements.

In this talk I introduce the construction of higher Kazhdan projections and compute the associated K-theory classes for certain groups, such as PSL_2(Z). This leads to several vanishing and non vanishing results for delocalised L²-Betti numbers.

This talk is based on joint work with Piotr Nowak and Kang Li as well as joint work with Hang Wang.