Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, January 4, 2016 - 12:00 to 13:00

Location:

Gilkey 115

Guest Speaker:

Dmytro Savchuk

Institution:

University of South Florida

Abstract:

This talk is cancelled due to campus closure for inclement weather. The class of Cayley automatic groups was recently introduced by Kharlampovich, Khoussainov and Miasnikov as a generalization of the class of automatic groups. This class retains many nice algorithmic properties of automatic groups, but is significantly wider. In particular, it includes many groups that are not finitely presented. One of the open questions about these groups is whether there is a Cayley automatic group of intermediate growth, or, equivalently, whether there is a group of intermediate growth whose Cayley graph is automatic. We give an example of a 4-regular infinite automatic graph of intermediate growth. It is constructed as a Schreier graph of a group generated by 3-state Mealy automaton. This is a joint work with Alexei Miasnikov.