WoG 2026 Talk 1.1: Kane Townsend - The isomorphism problem for virtually cyclic groups

Speaker: Kane Townsend Institution: University of Technology Sydney Title: The isomorphism problem for virtually cyclic groups Abstract: In 2018, Senizergues and Weiss established complexity bounds for the isomorphism problem for virtually free groups, where each group is given as a context-free grammar generating its word problem. In this talk, we consider the more restrictive class of virtually cyclic groups, with the aim of obtaining a sharper complexity bound. In 1991, Herbst proved that a group is virtually cyclic if and only if its word problem is accepted by a one-counter automaton. We therefore take as input one-counter automata accepting the word problems of the groups in question. This is joint work with Murray Elder and Adam Piggott.