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OverviewWe develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish strong uniformity results pertaining to zeta functions enumerating conjugacy classes of these groups. We deduce that the numbers of conjugacy classes of Fq-points of the groups under consideration depend polynomially on q. Our approach combines group theory, graph theory, toric geometry, and p-adic integration. Our uniformity results are in line with a conjecture of Higman on the numbers of conjugacy classes of unitriangular matrix groups. Our findings are, however, in stark contrast to related results by Belkale and Brosnan on the numbers of generic symmetric matrices of given rank associated with graphs. Full Product DetailsAuthor: Tobias Rossmann , Christopher VollPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: Volume: 294 Number: 1465 ISBN: 9781470468682ISBN 10: 1470468689 Pages: 120 Publication Date: 31 May 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1. Introduction 2. Ask zeta functions and modules over polynomial rings 3. Modules and module representations from (hyper)graphs 4. Modules over toric rings and associated zeta functions 5. Ask zeta functions of hypergraphs 6. Uniformity for ask zeta functions of graphs 7. Graph operations and ask zeta functions of cographs 8. Cographs, hypergraphs, and cographical groups 9. Further examples 10. Open problemsReviewsAuthor InformationTobias Rossmann, University of Galway, Ireland. Christopher Voll, Universitat Bielefeld, Germany. Tab Content 6Author Website:Countries AvailableAll regions |
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