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…
Algebraically hyperbolic groups
Giles Gardam, Dawid Kielak, Alan D. Logan
We initiate the study of torsion-free algebraically hyperbolic groups; these groups generalise torsion-free hyperbolic groups and are intricately related to groups with no Baumslag…
Target-wavelength-trimmed second harmonic generation with gallium phosphide-on-nitride ring resonators
Lillian Thiel, Alan D. Logan, Srivatsa Chakravarthi +4
We demonstrate post-fabrication target-wavelength trimming with a gallium phosphide on silicon nitride integrated photonic platform using controlled electron-beam exposure of hydro…
Variations on the Post Correspondence Problem for free groups
Laura Ciobanu, Alan D. Logan
The Post Correspondence Problem is a classical decision problem about equalisers of free monoid homomorphisms. We prove connections between several variations of this classical pro…
JSJ decompositions and polytopes for two-generator one-relator groups
Giles Gardam, Dawid Kielak, Alan D. Logan
We provide a direct connection between the Z_{max} (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianis…
Fixed points and stable images of endomorphisms for the free group of rank two
Laura Ciobanu, Alan D. Logan
We give an algorithm which computes the fixed subgroup and the stable image for any endomorphism of the free group of rank two , answering for a question posed by Stalli…
The equalizer conjecture for the free group of rank two
Alan D. Logan
The equaliser of a set of homomorphisms has rank at most two if contains an injective map, and is not finitely generated otherwise. This proves a s…
The Post Correspondence Problem and equalisers for certain free group and monoid morphisms
Laura Ciobanu, Alan D. Logan
A marked free monoid morphism is a morphism for which the image of each generator starts with a different letter, and immersions are the analogous maps in free groups. We show that…
400%/W second harmonic conversion efficiency in -diameter gallium phosphide-on-oxide resonators
Alan D. Logan, Michael Gould, Emma R. Schmidgall +7
Second harmonic conversion from 1550~nm to 775~nm with an efficiency of 400% W is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platfo…
The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions
Alan D. Logan
We classify finitely generated, residually finite automorphism-induced HNN-extensions in terms of the residual separability of a single associated subgroup. This classification pro…
Every group is the outer automorphism group of an HNN-extension of a fixed triangle group
Alan D. Logan
Fix an equilateral triangle group with arbitrary. Our main result is: for every presentation of every countable g…
On a question of Bumagin and Wise
Alan D. Logan
Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic fi…
The Bass-Jiang group for automorphism-induced HNN-extensions
Alan D. Logan
We use the Bass--Jiang group for automorphism-induced HNN-extensions to build a framework for the construction of tractable groups with pathological outer automorphism groups. We a…
On the outer automorphism groups of finitely generated, residually finite groups
Alan D. Logan
Bumagin-Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial…
The JSJ-decompositions of one-relator groups with torsion
Alan D. Logan
In this paper we use JSJ-decompositions to formalise a folk conjecture recorded by Pride on the structure of one-relator groups with torsion. We prove a slightly weaker version of…
The Outer Automorphism Groups of Two-Generator One-Relator Groups with Torsion
Alan D. Logan
The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recen…