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Dr Colin Reid

Postdoctoral Research Fellow

School of Mathematical and Physical Sciences

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 Expertise
My 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)

Fields of Research

Code Description Percentage
010105 Group Theory and Generalisations 100
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.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 117-130 (2018) [B1]
DOI 10.1017/9781108332675.008
Co-authors George Willis

Journal article (16 outputs)

Year Citation Altmetrics Link
2018 Reid CD, Wesolek PR, 'The essentially chief series of a compactly generated locally compact group', MATHEMATISCHE ANNALEN, 370 841-861 (2018) [C1]
DOI 10.1007/s00208-017-1597-0
Citations Scopus - 2Web of Science - 1
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)

© 2017 London Mathematical Society In The essentially chief series of a compactly generated locally compact group, an analogue of chief series for finite groups is discovered for ... [more]

© 2017 London Mathematical Society In The essentially chief series of a compactly generated locally compact group, an analogue of chief series for finite groups is discovered for compactly generated locally compact groups. In the present article, we show that chief factors necessarily exist in all locally compact groups with sufficiently rich topological structure. We also show that chief factors have one of seven types, and for all but one of these types, there is a decomposition into discrete groups, compact groups, and topologically simple groups. Our results for chief factors require exploring the theory developed in Chief factors in Polish groups in the setting of locally compact groups. In this context, we obtain tighter restrictions on the factorization of normal compressions and the structure of quasi-products. Consequently, both (non-)amenability and elementary decomposition rank are preserved by normal compressions.

DOI 10.1112/plms.12088
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]
DOI 10.1016/j.jfluidstructs.2016.11.012
Citations Scopus - 1Web of Science - 1
Co-authors Mike Meylan
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]
DOI 10.1017/fms.2017.9
Citations Web of Science - 2
Co-authors George Willis
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]
DOI 10.1017/fms.2017.8
Citations Web of Science - 3
Co-authors George Willis
2016 Reid CD, 'Dynamics of flat actions on totally disconnected, locally compact groups', NEW YORK JOURNAL OF MATHEMATICS, 22 115-190 (2016) [C1]
2015 Reid CD, 'THE NUMBER OF PROFINITE GROUPS WITH A SPECIFIED SYLOW SUBGROUP', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 99 108-127 (2015) [C1]
DOI 10.1017/S1446788714000834
2014 Reid CD, 'Endomorphisms of profinite groups', GROUPS GEOMETRY AND DYNAMICS, 8 553-564 (2014) [C1]
DOI 10.4171/GGD/238
Citations Scopus - 1Web of Science - 1
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]
Citations Scopus - 7Web of Science - 7
Co-authors George Willis
2013 Reid CD, 'THE GENERALISED PRO-FITTING SUBGROUP OF A PROFINITE GROUP', COMMUNICATIONS IN ALGEBRA, 41 294-308 (2013) [C1]
DOI 10.1080/00927872.2011.629269
Citations Scopus - 2Web of Science - 3
2013 Reid CD, 'Local Sylow theory of totally disconnected, locally compact groups', JOURNAL OF GROUP THEORY, 16 535-555 (2013) [C1]
DOI 10.1515/jgt-2013-0005
Citations Scopus - 2Web of Science - 2
2013 Caprace P-E, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657-661 (2013) [C1]
DOI 10.1016/j.crma.2013.09.010
Citations Scopus - 4Web of Science - 5
Co-authors George Willis
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.

DOI 10.1112/blms/bdr099
Citations Scopus - 3
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).

DOI 10.1007/s00013-011-0226-5
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.

DOI 10.1016/j.jalgebra.2010.07.033
Citations Scopus - 2
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.

DOI 10.1016/j.jalgebra.2010.07.034
Citations Scopus - 4
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Grants and Funding

Summary

Number of grants 2
Total funding $304,022

Click on a grant title below to expand the full details for that specific grant.


20161 grants / $10,668

DVC(RI) Research Support for DECRA (DE15)$10,668

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
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News

ARC DECRA funding success

November 18, 2014

Dr Colin D Reid has been awarded more than $280,000 for his project Branching and self-similarity in group actions.

Dr Colin Reid

Position

Postdoctoral Research Fellow
School of Mathematical and Physical Sciences
Faculty of Science

Contact Details

Email colin.d.reid@newcastle.edu.au
Phone (02) 4921 6280

Office

Room V223
Building V Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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