Bianca Marchionna (Bielefeld University/Milano-Bicocca) has visited the Charlotte Scott Centre for Algebra during the week starting on the 12th of February for a research visit. During her stay, Bianca presented her work at our algebra seminar and had several discussions with Lincoln algebraists on questions of mutual interest.
Talk title: Double-coset zeta functions and groups acting on trees
Abstract: The double-coset zeta functions have been recently introduced by I. Castellano, G. Chinello and T. Weigel as a possible tool for studying asymptotic properties of a locally compact group G. These functions are defined by Dirichlet series, with each series corresponding to a compact open subgroup U of G. They arise from counting the U-double-cosets of G with a prescribed Haar measure.
The seminar focuses on the favourable case of G acting on a locally finite tree. If the action is either “sufficiently transitive” or “(P)-closed”, one can reduce the study of the series to handle combinatorial problems involving local data of the actions.
We also present a criterion on these groups to relate their Euler-Poincaré characteristic with the value of the above-mentioned zeta functions at -1.
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