Analysis and Probability Seminar

Abstract: For a discrete group G, higher Kazhdan projections are 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. Employing these projections we define delocalised L²-Betti numbers for discrete groups, in analogy with their usual l²-Betti numbers. However computations remain challenging as there are no tools available yet. Describing explicitly the K-theory class of higher Kazhdan projections is a promising approach to this problem.

In this talk I introduce the construction of higher Kazhdan projections and compute the associated K-theory classes for virtually free groups. This leads to several vanishing and non-vanishing results for delocalised L²-Betti numbers.

This talk is based on work in progress with Hang Wang.