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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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The tree lattice existence theorems
by
Lisa Carbone
Rutgers, The State University of New Jersey

Let X be a locally finite tree. Then G=Aut(X) is a locally compact group. Bass and Lubotzky asked the following question: When does G contain lattices, that is, discrete subgroups of finite covolume? The answer to the question is difficult and complicated but in this talk we discuss a complete answer to the question, answering several conjectures that were formulated by Bass and Lubotzky. Our general strategy is to show that lattices exist by providing explicit constructions of them. The techniques involve an interesting mix of group theory, both finite and infinite, and graph theory.

Date received: March 13, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-86.