67 citations · 103 across the 16 of their papers we have counts for
21 papers
Fixed subgroups of generalised Baumslag-Solitar groups
Oli Jones, Alan Logan
We investigate fixed subgroups of automorphisms of generalised Baumslag-Solitar (GBS) groups. Our main results are for automorphisms leaving a Bass-Serre tree invariant, under the…
Selective active resonance tuning for multi-mode nonlinear photonic cavities
Alan D. Logan, Nicholas S. Yama, Kai-Mei C. Fu
Resonant enhancement of nonlinear photonic processes is critical for the scalability of applications such as long-distance entanglement generation. To implement nonlinear resonant…
Post's correspondence problem for hyperbolic and virtually nilpotent groups
Laura Ciobanu, Alex Levine, Alan D. Logan
Post's Correspondence Problem (the PCP) is a classical decision problem in theoretical computer science that asks whether for pairs of free monoid morphisms t…
The Conjugacy Problem for ascending HNN-extensions of free groups
Alan D. Logan
We give an algorithm to solve the Conjugacy Problem for ascending HNN-extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group…
Triply-Resonant Sum Frequency Conversion with Gallium Phosphide Ring Resonators
Alan D. Logan, Shivangi Shree, Srivatsa Chakravarthi +5
We demonstrate quasi-phase matched, triply-resonant sum frequency conversion in 10.6-um-diameter integrated gallium phosphide ring resonators. A small-signal, waveguide-to-waveguid…
The Surface Group Conjectures for groups with two generators
Giles Gardam, Dawid Kielak, Alan D. Logan
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups…