Dr Colin Reid
Postdoctoral Research Fellow
School of Information and Physical Sciences
 Email:colin.d.reid@newcastle.edu.au
 Phone:(02) 4921 6280
Career Summary
Biography
I completed my PhD at Queen Mary, University of London in 2010, which was on topics in profinite group theory. Since then, I have worked as a fulltime researcher in Germany, Belgium and Australia, with my research focus shifting from profinite groups to the more general class of totally disconnected, locally compact groups. I began working at the University of Newcastle in August 2012 as a research associate working on the Discovery Project "Theory and applications of symmetries of relational structures" (DP120100996, CIs: George Willis and Murray Elder).
Research ExpertiseMy research is in the area of topological group theory, especially totally disconnected, locally compact groups.
Teaching Expertise
I gave a thirdyear course in Algebra (MATH3120) in 2013 and 2014.
Administrative Expertise
N/A
Collaborations
I have recently worked with George Willis at Newcastle and PierreEmmanuel Caprace at the Université catholique de Louvain in Belgium.
Qualifications
 PhD, University of London
 Bachelor of Arts, University of Cambridge  UK
Keywords
 Algebra
 Group Theory
Languages
 German (Fluent)
 French (Fluent)
Fields of Research
Code  Description  Percentage 

490405  Group theory and generalisations  100 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Chapter (1 outputs)
Year  Citation  Altmetrics  Link  

2018 
Reid C, Willis G, 'Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups', New Directions in Locally Compact Groups, Cambridge University Press, Cambridge, UK 117130 (2018) [B1]

Journal article (24 outputs)
Year  Citation  Altmetrics  Link  

2021 
Reid CD, Wesolek PR, Le Maître F, 'Chief factors in Polish groups', Mathematical Proceedings of the Cambridge Philosophical Society, (2021) In finite group theory, chief factors play an important and wellunderstood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the devel... [more] In finite group theory, chief factors play an important and wellunderstood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the development of this theory, we prove a version of the Schreier refinement theorem. We also prove a trichotomy for the structure of topologically characteristically simple Polish groups. The development of the theory of chief factors requires two independently interesting lines of study. First we consider injective, continuous homomorphisms with dense normal image. We show such maps admit a canonical factorisation via a semidirect product, and as a consequence, these maps preserve topological simplicity up to abelian error. We then define two generalisations of direct products and use these to isolate a notion of semisimplicity for Polish groups.


2021 
Garrido A, Reid CD, 'Discrete locally finite full groups of Cantor set homeomorphisms', BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, (2021)


2021 
Reid CD, 'A classification of the abelian minimal closed normal subgroups of locally compact secondcountable groups', Journal of Group Theory, 24 509531 (2021) [C1]


2020 
Reid CD, 'Equicontinuity, orbit closures and invariant compact open sets for group actions on zerodimensional spaces', GROUPS GEOMETRY AND DYNAMICS, 14 413425 (2020) [C1]


2020 
Groenhout P, Reid CD, Willis GA, 'Topologically simple, totally disconnected, locally compact infinite matrix groups', Journal of Lie Theory, 30 965980 (2020) [C1] We construct uncountably many nonlocally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known e... [more] We construct uncountably many nonlocally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known examples of such groups in that they have trivial quasicentre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost uppertriangular matrices modulo scalar matrices over finite fields, where 'almost uppertriangular' is defined with respect to one of an uncountable family of preorders generalising the orders (Z, =) and (N, =).


2020 
Reid CD, 'Distal actions on coset spaces in totally disconnected locally compact groups', Journal of Topology and Analysis, 12 491532 (2020) [C1] Let G be a totally disconnected locally compact (t.d.l.c.) group and let H be an equicontinuously (for example, compactly) generated group of automorphisms of G. We show that ever... [more] Let G be a totally disconnected locally compact (t.d.l.c.) group and let H be an equicontinuously (for example, compactly) generated group of automorphisms of G. We show that every distal action of H on a coset space of G is a SIN action, with the small invariant neighborhoods arising from open Hinvariant subgroups. We obtain a number of consequences for the structure of the collection of open subgroups of a t.d.l.c. group. For example, it follows that for every compactly generated subgroup K of G, there is a compactly generated open subgroup E of G such that K = E and such that every open subgroup of G containing a finite index subgroup of K contains a finite index subgroup of E. We also show that for a large class of closed subgroups L of G (including for instance all closed subgroups L such that L is an intersection of subnormal subgroups of open subgroups), every compactly generated open subgroup of L can be realized as L ? O for an open subgroup of G.


2019 
Reid CD, Wesolek PR, 'Homomorphisms into totally disconnected, locally compact groups with dense image', Forum Mathematicum, 31 685701 (2019) [C1]


2018 
Reid CD, Wesolek PR, 'Dense normal subgroups and chief factors in locally compact groups', PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 116 760812 (2018) [C1]


2018 
Reid CD, Wesolek PR, 'The essentially chief series of a compactly generated locally compact group', MATHEMATISCHE ANNALEN, 370 841861 (2018) [C1]


2017 
Wolgamot HA, Meylan MH, Reid CD, 'Multiply heaving bodies in the timedomain: Symmetry and complex resonances', JOURNAL OF FLUIDS AND STRUCTURES, 69 232251 (2017) [C1]


2017 
Caprace PE, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART I: GENERAL THEORY', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]


2017 
Caprace PE, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]


2016 
Reid CD, 'Dynamics of flat actions on totally disconnected, locally compact groups', NEW YORK JOURNAL OF MATHEMATICS, 22 115190 (2016) [C1]


2015 
Reid CD, 'THE NUMBER OF PROFINITE GROUPS WITH A SPECIFIED SYLOW SUBGROUP', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 99 108127 (2015) [C1]


2014 
Reid CD, 'Endomorphisms of profinite groups', GROUPS GEOMETRY AND DYNAMICS, 8 553564 (2014) [C1]


2014 
Caprace PE, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957967 (2014) [C1]


2013 
Reid CD, 'THE GENERALISED PROFITTING SUBGROUP OF A PROFINITE GROUP', COMMUNICATIONS IN ALGEBRA, 41 294308 (2013) [C1]


2013 
Reid CD, 'Local Sylow theory of totally disconnected, locally compact groups', JOURNAL OF GROUP THEORY, 16 535555 (2013) [C1]


2013 
Caprace PE, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657661 (2013) [C1]


2012 
Reid CD, 'Inverse system characterizations of the (hereditarily) just infinite property in profinite groups', Bulletin of the London Mathematical Society, 44 413425 (2012) [C1] We give criteria on an inverse system of finite groups that ensure that the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'univ... [more] We give criteria on an inverse system of finite groups that ensure that the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'universal' in that all (hereditarily) just infinite profinite groups arise as limits of the specified form. Inspired by a recent paper of Wilson, we give special consideration to (hereditarily) just infinite profinite groups that are not virtually prop. © 2011 London Mathematical Society.


2011 
Reid CD, 'On finite groups whose Sylow subgroups have a bounded number of generators', Archiv der Mathematik, 96 207214 (2011) [C1] Let G be a finite nonnilpotent group such that every Sylow subgroup of G is generated by at most d elements, and such that p is the largest prime dividing {pipe}G{pipe}. We show ... [more] Let G be a finite nonnilpotent group such that every Sylow subgroup of G is generated by at most d elements, and such that p is the largest prime dividing {pipe}G{pipe}. We show that G has a nonnilpotent image G/N, such that N is characteristic and of index bounded by a function of d and p. This result will be used to prove that G has a nilpotent normal subgroup of index bounded in terms of d and p. © 2011 The Author(s).


2010 
Reid CD, 'Subgroups of finite index and the just infinite property', Journal of Algebra, 324 22192222 (2010) A residually finite (profinite) group G is just infinite if every nontrivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining whi... [more] A residually finite (profinite) group G is just infinite if every nontrivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining which (closed) subgroups of finite index of a just infinite group are themselves just infinite. If G is just infinite and not virtually abelian, we show that G is hereditarily just infinite if and only if all maximal (closed) subgroups of finite index are just infinite. This result will be used to show that a finitely generated prop group G is just infinite if and only if G has no nontrivial finite normal subgroups and F(G) has a just infinite open subgroup. © Elsevier Inc.


2010 
Reid CD, 'On the structure of just infinite profinite groups', Journal of Algebra, 324 22492261 (2010) A profinite group G is just infinite if every closed normal subgroup of G is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every ... [more] A profinite group G is just infinite if every closed normal subgroup of G is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup H of G, there are only finitely many open normal subgroups of G not contained in H. This extends a result recently established by Barnea, Gavioli, JaikinZapirain, Monti and Scoppola (2009) in [1], who proved the same characterisation in the case of prop groups. We also use this result to establish a number of features of the general structure of profinite groups with regard to the just infinite property. © Elsevier Inc.


Show 21 more journal articles 
Grants and Funding
Summary
Number of grants  2 

Total funding  $304,021 
Click on a grant title below to expand the full details for that specific grant.
20161 grants / $10,667
DVC(RI) Research Support for DECRA (DE15)$10,667
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Doctor Colin Reid 
Scheme  DECRA Support 
Role  Lead 
Funding Start  2016 
Funding Finish  2017 
GNo  G1600219 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
20151 grants / $293,354
Branching and selfsimilarity in group actions$293,354
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Doctor Colin Reid 
Scheme  Discovery Early Career Researcher Award (DECRA) 
Role  Lead 
Funding Start  2015 
Funding Finish  2017 
GNo  G1400272 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
Research Supervision
Number of supervisions
Current Supervision
Commenced  Level of Study  Research Title  Program  Supervisor Type 

2021  PhD  Exploring Smith’s Construction to Generate Local Isomorphism Classes  PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle  CoSupervisor 
2021  Masters  Unitary Representations of Automorphism Groups of LabelRegular Trees  M Philosophy (Mathematics), College of Engineering, Science and Environment, The University of Newcastle  CoSupervisor 
2019  PhD  A Finer Invariant for Locally Compact Totally Disconnected Groups  PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle  CoSupervisor 
News
ARC DECRA funding success
November 18, 2014
Dr Colin Reid
Position
Postdoctoral Research Fellow
School of Information and Physical Sciences
College of Engineering, Science and Environment
Contact Details
colin.d.reid@newcastle.edu.au  
Phone  (02) 4921 6280 
Mobile  0435520759 
Office
Room  V223 

Building  V Mathematics Building 
Location  Callaghan University Drive Callaghan, NSW 2308 Australia 