
Dr Colin Reid
Postdoctoral Research Fellow
School of Mathematical 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 full-time 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 third-year course in Algebra (MATH3120) in 2013 and 2014.
Administrative Expertise
N/A
Collaborations
I have recently worked with George Willis at Newcastle and Pierre-Emmanuel 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)
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Chapter (1 outputs)
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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 117-130 (2018) [B1]
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Journal article (21 outputs)
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2020 |
Reid CD, 'Equicontinuity, orbit closures and invariant compact open sets for group actions on zero-dimensional spaces', GROUPS GEOMETRY AND DYNAMICS, 14 413-425 (2020)
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2020 |
Groenhout P, Reid CD, Willis GA, 'Topologically simple, totally disconnected, locally compact infinite matrix groups', Journal of Lie Theory, 30 965-980 (2020) We construct uncountably many non-locally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known e... [more] We construct uncountably many non-locally 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 quasi-centre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost upper-triangular matrices modulo scalar matrices over finite fields, where 'almost upper-triangular' is defined with respect to one of an uncountable family of preorders generalising the orders (Z, =) and (N, =).
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2020 |
Reid CD, 'A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups', Journal of Group Theory, (2020) We classify the locally compact second-countable (l.c.s.c.) groups A that are abelian and topologically characteristically simple. All such groups A occur as the monolith of some ... [more] We classify the locally compact second-countable (l.c.s.c.) groups A that are abelian and topologically characteristically simple. All such groups A occur as the monolith of some soluble l.c.s.c. group G of derived length at most 3; with known exceptions (specifically, when A is Qn or its dual for some n ¿ N), we can take G to be compactly generated. This amounts to a classification of the possible isomorphism types of abelian chief factors of l.c.s.c. groups, which is of particular interest for the theory of compactly generated locally compact groups.
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2020 |
Reid CD, 'Distal actions on coset spaces in totally disconnected locally compact groups', Journal of Topology and Analysis, 12 491-532 (2020) 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 H-invariant 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.
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2019 |
Reid CD, Wesolek PR, 'Homomorphisms into totally disconnected, locally compact groups with dense image', Forum Mathematicum, 31 685-701 (2019) [C1]
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2018 |
Reid CD, Wesolek PR, 'Dense normal subgroups and chief factors in locally compact groups', PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 116 760-812 (2018) [C1]
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2018 |
Reid CD, Wesolek PR, 'The essentially chief series of a compactly generated locally compact group', MATHEMATISCHE ANNALEN, 370 841-861 (2018) [C1]
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2017 |
Wolgamot HA, Meylan MH, Reid CD, 'Multiply heaving bodies in the time-domain: Symmetry and complex resonances', JOURNAL OF FLUIDS AND STRUCTURES, 69 232-251 (2017) [C1]
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2017 |
Caprace P-E, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART I: GENERAL THEORY', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]
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2017 |
Caprace P-E, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]
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2016 |
Reid CD, 'Dynamics of flat actions on totally disconnected, locally compact groups', NEW YORK JOURNAL OF MATHEMATICS, 22 115-190 (2016) [C1]
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2015 |
Reid CD, 'THE NUMBER OF PROFINITE GROUPS WITH A SPECIFIED SYLOW SUBGROUP', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 99 108-127 (2015) [C1]
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2014 |
Reid CD, 'Endomorphisms of profinite groups', GROUPS GEOMETRY AND DYNAMICS, 8 553-564 (2014) [C1]
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2014 |
Caprace P-E, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957-967 (2014) [C1]
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2013 |
Reid CD, 'THE GENERALISED PRO-FITTING SUBGROUP OF A PROFINITE GROUP', COMMUNICATIONS IN ALGEBRA, 41 294-308 (2013) [C1]
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2013 |
Reid CD, 'Local Sylow theory of totally disconnected, locally compact groups', JOURNAL OF GROUP THEORY, 16 535-555 (2013) [C1]
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2013 |
Caprace P-E, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657-661 (2013) [C1]
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2012 |
Reid CD, 'Inverse system characterizations of the (hereditarily) just infinite property in profinite groups', Bulletin of the London Mathematical Society, 44 413-425 (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 pro-p. © 2011 London Mathematical Society.
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2011 |
Reid CD, 'On finite groups whose Sylow subgroups have a bounded number of generators', Archiv der Mathematik, 96 207-214 (2011) [C1] Let G be a finite non-nilpotent 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 non-nilpotent 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 non-nilpotent 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).
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2010 |
Reid CD, 'Subgroups of finite index and the just infinite property', Journal of Algebra, 324 2219-2222 (2010) A residually finite (profinite) group G is just infinite if every non-trivial (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 non-trivial (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 pro-p group G is just infinite if and only if G has no non-trivial finite normal subgroups and F(G) has a just infinite open subgroup. © Elsevier Inc.
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2010 |
Reid CD, 'On the structure of just infinite profinite groups', Journal of Algebra, 324 2249-2261 (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, Jaikin-Zapirain, Monti and Scoppola (2009) in [1], who proved the same characterisation in the case of pro-p 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.
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Show 18 more journal articles |
Grants and Funding
Summary
Number of grants | 2 |
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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 |
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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 self-similarity 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 |
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2021 | Masters | Unitary Representations of Automorphism Groups of Label-Regular Trees | M Philosophy (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Co-Supervisor |
2019 | PhD | A Finer Invariant for Locally Compact Totally Disconnected Groups | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Co-Supervisor |
News
ARC DECRA funding success
November 18, 2014
Dr Colin Reid
Position
Postdoctoral Research Fellow
School of Mathematical and Physical Sciences
College of Engineering, Science and Environment
Contact Details
colin.d.reid@newcastle.edu.au | |
Phone | (02) 4921 6280 |
Office
Room | V223 |
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Building | V Mathematics Building |
Location | Callaghan University Drive Callaghan, NSW 2308 Australia |