Ph.D. Program in Mathematics upcoming Defense of Dissertations:
Note: If you are interested in “attending” a remote defense, send an email to the student and/or Dissertation Chair (Advisor) for remote access details. If no response, contact Mathematics@gc.cuny.edu.
Name: Christopher Natoli
Title: Some Model Theory of Free Groups
Defense Date: Tuesday, June 30, 2020
Location: Zoom (Contact Student or Committee Chair for link)
Committee Chair: Olga Kharlampovich, The Graduate Center & Hunter College
Committee Member 2: Ilya Kapovich, The Graduate Center & Hunter College
Committee Member 3: Vladimir Shpilrain, The Graduate Center & City College
Abstract: There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not universally homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form universal Fraisse classes and that the class of non-abelian limit groups fails to form a strong universal Fraisse class. The second main result is that if a countable group is elementarily equiv-alent to a non-abelian free group and all of its finitely generated abelian subgroups are cyclic, then the group is a union of a chain of regular NTQ groups (i.e., hyperbolic towers).