Dr Colin Reid
Honorary Lecturer
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 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). I was an ARC DECRA Fellow in 2015-17. From 2018 onwards I have been a postdoctoral research fellow associated to the research project "Zero-Dimensional Symmetry and its Ramifications" led by ARC Laureate Fellow Prof George Willis.
Research Expertise
My research is in the area of topological group theory, especially totally disconnected, locally compact groups.
Teaching Expertise
I have a range of teaching experience at the undergraduate and postgraduate level. I have lectured introductory courses (MATH1001, 2019; MATH1002, 2022; MATH1120) and more advanced undergraduate courses (MATH3120 Algebra, 2013-14, MATH3242 Complex Analysis, 2016). I have also delivered graduate-level courses in my field of research, including an AMSI ACE Honours Course on Topological Groups (2015) and short courses at the "Winter of Disconnectedness" series of workshops hosted by the universities of Newcastle, Melbourne and Sydney in 2016, and a programme at the Bernoulli Center in Switzerland in 2020.
I am currently supervising two PhD students and have supervised a Master's student.
Administrative Expertise
I have been course coordinator for some of the courses I have lectured. I was also one of the organisers of the 2016 "Winter of Disconnectedness" series of workshops and the 2020 Bernoulli programme, and I am involved in organising an upcoming special semester at the University of Münster to take place in 2023.
Collaborations
I have past and ongoing collaborations with researchers in a number of countries, including: George Willis (Australia), Pierre-Emmanuel Caprace (Belgium), Phillip Wesolek (USA), Simon Smith (UK), Timothée Marquis (Belgium), Alejandra Garrido (Spain) and Adrien Le Boudec (France).
Qualifications
- PhD, University of London
- Bachelor of Arts, University of Cambridge - UK
Keywords
- Algebra
- Automorphisms of discrete structures
- Group Theory
- Topological Groups
Languages
- German (Fluent)
- French (Fluent)
Fields of Research
Code | Description | Percentage |
---|---|---|
490404 | Combinatorics and discrete mathematics (excl. physical combinatorics) | 10 |
490405 | Group theory and generalisations | 90 |
Professional Experience
Academic appointment
Dates | Title | Organisation / Department |
---|---|---|
1/1/2024 - | Postdoctoral researcher | Ecole Normale Supérieure De Lyon France |
1/9/2023 - 30/11/2023 | Friedrich Wilhelm Bessel visiting fellow | University of Münster Germany |
1/1/2018 - 31/8/2023 | Postdoctoral Research Fellow | School of Mathematical and Physical Sciences, The University of Newcastle Australia |
1/1/2015 - 31/12/2017 | ARC DECRA Fellow | School of Mathematical and Physical Sciences, The University of Newcastle Australia |
1/8/2012 - 31/12/2014 | Postdoctoral Researcher | School of Mathematical and Physical Sciences, The University of Newcastle Australia |
1/4/2011 - 31/7/2012 | Postdoctoral Researcher | Université Catholique De Louvain Belgium |
1/10/2010 - 31/3/2011 | Research Associate | University of Göttingen Germany |
1/4/2010 - 30/9/2010 | Research Associate | Aachen University Germany |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Chapter (2 outputs)
Year | Citation | Altmetrics | Link | |||||
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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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2018 |
Reid CD, 'Normal Subgroup Structure of Totally Disconnected Locally Compact Groups', MATRIX Book Series, Springer International Publishing, Cham 525-560 (2018) [B1]
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Nova |
Journal article (31 outputs)
Year | Citation | Altmetrics | Link | ||||||||
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2024 |
Caprace P-E, Marquis T, Reid CD, 'Growing trees from compact subgroups', GROUPS GEOMETRY AND DYNAMICS, 18 327-352 (2024) [C1]
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2024 |
Reid CD, 'Multiple transitivity except for a system of imprimitivity', Journal of Group Theory, (2024) [C1] Let ¿ be a set equipped with an equivalence relation~ we refer to the equivalence classes as blocks of ¿. A permutation groupG = Sym (¿) G = {Sym}(O) is-by-block-Transitive if~ is... [more] Let ¿ be a set equipped with an equivalence relation~ we refer to the equivalence classes as blocks of ¿. A permutation groupG = Sym (¿) G = {Sym}(O) is-by-block-Transitive if~ isinvariant, with at least blocks, and G is transitive on the set of-Tuples of points such that no two entries lie in the same block. The action is block-faithful if the action on the set of blocks is faithful. In this article, we classify the finite block-faithful 2-by-block-Transitive actions. We also show that, fork = 3 k\geq 3, there are no finite block-faithful-by-block-Transitive actions with nontrivial blocks.
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2023 |
Reid CD, 'Totally disconnected locally compact groups with just infinite locally normal subgroups', Israel Journal of Mathematics, (2023) [C1] We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are locally isomorphic to a just infinite profinite group, building on an earlier r... [more] We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are locally isomorphic to a just infinite profinite group, building on an earlier result of Barnea¿Ershov¿Weigel and also using tools developed by P.-E. Caprace, G. Willis and the author for studying local structure in t.d.l.c. groups. The approach uses the following property of just infinite profinite groups, essentially due to Wilson: given a locally normal subgroup K of G, then there is an open subgroup of K that is a direct factor of an open subgroup of G. This is a local property of t.d.l.c. groups and we obtain a characterization of the local isomorphism types of t.d.l.c. groups that have it.
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2022 |
Reid CD, 'ORIENTATION of PIECEWISE POWERS of A MINIMAL HOMEOMORPHISM', Journal of the Australian Mathematical Society, 113 226-256 (2022) [C1] We show that, given a compact minimal system and an element h of the topological full group of g, the infinite orbits of h admit a locally constant orientation with respect to the... [more] We show that, given a compact minimal system and an element h of the topological full group of g, the infinite orbits of h admit a locally constant orientation with respect to the orbits of g. We use this to obtain a clopen partition of into minimal and periodic parts, where G is any virtually polycyclic subgroup of. We also use the orientation of orbits to give a refinement of the index map and to describe the role in of the submonoid generated by the induced transformations of g. Finally, we consider the problem, given a homeomorphism h of the Cantor space X, of determining whether or not there exists a minimal homeomorphism g of X such that.
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2022 |
Caprace P-E, Marquis T, Reid CD, 'Locally normal subgroups and ends of locally compact Kac-Moody groups', MUENSTER JOURNAL OF MATHEMATICS, 15 473-498 (2022) [C1]
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2022 |
Reid CD, 'Decomposition of locally compact coset spaces', JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 107 407-440 (2022) [C1]
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2022 |
Reid CD, Wesolek PR, Maître FL, 'Chief factors in Polish groups', Mathematical Proceedings of the Cambridge Philosophical Society, 173 239-296 (2022) [C1] In finite group theory, chief factors play an important and well-understood 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 well-understood 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.
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2021 |
Caprace P-E, Reid C, Wesolek P, 'Approximating Simple Locally Compact Groups by Their Dense Locally Compact Subgroups', INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021 5037-5110 (2021) [C1]
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2021 |
Garrido A, Reid CD, 'Discrete locally finite full groups of Cantor set homeomorphisms', BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 53 1228-1248 (2021) [C1]
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2021 |
Reid CD, 'A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups', Journal of Group Theory, 24 509-531 (2021) [C1]
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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) [C1]
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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) [C1] 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 |
Caprace P-E, Kropholler PH, Reid CD, Wesolek P, 'On the residual and profinite closures of commensurated subgroups', MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 169 411-432 (2020) [C1]
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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) [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 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 28 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 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 |
---|---|---|---|---|
2021 | PhD | Universal Covers of Rooted Graphs and Their Higman-Thompson Groups | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Co-Supervisor |
2019 | PhD | Elementary Topological Groups | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Co-Supervisor |
Past Supervision
Year | Level of Study | Research Title | Program | Supervisor Type |
---|---|---|---|---|
2024 | Masters | On the Unitary Representation Theory of Contraction Groups | M Philosophy (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Co-Supervisor |
News
News • 18 Nov 2014
ARC DECRA funding success
Dr Colin D Reid has been awarded more than $280,000 in ARC Discovery Early Career Researcher Award (DECRA) funding commencing in 2015 for his research project Branching and self-similarity in group actions.
Dr Colin Reid
Position
Honorary Lecturer
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 | V-223 |
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Building | V Mathematics Building |
Location | Callaghan University Drive Callaghan, NSW 2308 Australia |