South England Profinite Groups Meetings

Joint Research Group funded by LMS Scheme 3
Academic Year 2013-14


  • Background: Profinite and asymptotic methods have been successfully applied to general problems of group theory. In addition there are interesting links to number theory, geometry and other areas.

  • Activities: During the academic year 2013-14 we are holding two meetings in order to

    - provide a platform for young mathematicians from across the south of England to meet and discuss their research in profinite groups, asymptotic group theory and related topics,

    - get graduate students and postdoctoral fellows involved by giving them the opportunity to discuss and possibly present their individual work,

    - give the participants an opportunity to widen their research horizons and their knowledge base by familiarising themselves with research adjacent to their own,

    - foster and develop collaborative links both within the group and with selected experts from the UK and abroad.

  • Additional Meeting: This year we hold only two meetings. However, the 2014 BMC at Queen Mary, London which is held on 7-10 April 2014 includes a workshop on group theory organized by John Bray (Queen Mary) and Nikolay Nikolov (University of Oxford).

  • Participants: We welcome and encourage interested mathematicians at all levels to join us in our meetings.
    The Joint Research Group receives financial support from the London Mathematical Society and has therefore limited funds to reimburse travel expenses of UK-based students and young mathematicians. Please contact the organisers if you wish to apply for such reimbursements.

    For UK-based mathematicians with parental duties the LMS has a scheme which allows participants of meetings like ours to apply for a supplementary grant to help covering childcare costs; see here for further information.

  • Organisers: Corresponding organisers of the Joint Research Group are Brita Nucinkis (Royal Holloway, University of London), Rachel Camina (University of Cambridge) and Nikolay Nikolov (Univesity of Oxford).

  • Web Site: http://www.ma.rhul.ac.uk/sepgm/ brings you to this page.
 Symmetry



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Calendar of Events

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Next Meeting

Mackey structures for finite, infinite and profinite groups

13 June 2014 at Royal Holloway, University of London

  • Description: Mackey functors have been studied extensively for finite groups. In this meeting we will give an introduction to the subject and will look at recent applications for finite, infinite and profinite groups.

  • Schedule:

    12:00-12:30  Introduction to Mackey functors, Brita Nucinkis (Royal Holloway)

    12:30-13:15 Lunch

    13:15 – 14:15 Mackey functors for finite groups, Peter Symonds (Manchester)

    14:30 – 15:30 Cohomological dimension invariants for Mackey functors of infinite groups and their geometric interpretation, Dieter Degrijse (Copenhagen)

    15:30 – 16:00 Coffee

    16:00 – 17:00 Cohomological Mackey functors for profinite groups, Thomas Weigel (Milan-Bicocca)

    Evening: Pub and dinner

  • Speakers: Brita Nucinkis (Royal Holloway), Peter Symonds (Manchester), Dieter Degrijse (Copenhagen) and Thomas Weigel (Milan-Bicocca)

  • Abstracts:

    Cohomological dimension invariants for Mackey functors of infinite groups and their geometric interpretation,
    Dieter Degrijse: I will recall the notion of Mackey cohomological dimension of an in nite discrete group introduced by Martinez-Perez and Nucinkis, and discuss its relationship with more classical cohomological invariants such as the virtual cohomological dimension and the Bredon cohomological dimension for proper actions. In the second part of the talk I will report on work in progress joint with Barcenas and Patchkoria where we try to nd a suitable geometric interpretation for the Mackey cohomological dimension. This leads us into the world of equivariant stable homotopy theory.

    Cohomological Mackey functors for profinite groups
    , Thomas Weigel: (Cohomological) Mackey functors for finite or profinite groups can be defined in several equivalent ways. For several applications in group theory it seems to be convenient to consider cohomological Mackey functors rather than just Mackey functors. For cohomological Mackey functors it is possible to introduce a “section cohomology theory” allowing to introduce notions like “Galois-descent” (or “co-Galois descent”) and the “Hilbert 90 property”.

    In the lecture we will start from the definition and will illustrate how the section cohomology groups arise in this context. Establishing several properties of these cohomology groups will allow us to apply this theory in the context of pro-p groups. The intention is to discuss
    briefly the following topics:
    - A. Brumer’s characterisation of pro-p groups G satisfying scd(G) at most 2;
    - characterising free pro-p groups by elementary abelian quotients;
    - Stallings’ decomposition theorem for finitely generated pro-p groups;
    - a special case of the elementary type conjecture.

  • Location: McCrea Buliding (Department of Matheamtics) room C219, Royal Holloway

  • Travel Support : Limited funds are available to reimburse travel expenses of UK-based students and other young mathematicians.

  • Date: 13 June 2014 at 12:00-17:00

  • Local Organiser: Yiftach Barnea and Brita Nucinkis

  • Support for the Meeting: The meeting is funded by the LMS Scheme 3 and Department of Mathematics, Royal Holloway, University of London
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Complete Calendar of Events

One-Day Meeting: Conjugacy classes and related topics

  • Description: Conjugacy classes give useful structural information about groups, just how much information the classes, or their sizes, infer is an interesting problem. In this meeting we will look at known results and further questions, both in the finite and infinite setting.
  • Speakers: Rachel Camina (Cambridge) or Alan Camina (UEA), Ben Martin (Auckland) , Dan Segal (Oxford), Christopher Voll (Bielefeld).
  • Location: University of Cambridge
  • Date:13 December 2013
  • Local Organiser: Rachel Camina

One-Day Meeting: Mackey Functors for Finite and Infinite Groups

  • Description: TBA
  • Speakers include: Dieter Degrijse (Copenhagen) and Peter Symonds (Manchenster)
  • Location: Royal Holloway, University of London
  • Date: June 2014
  • Local Organiser: Yiftach Barnea and Brita Nucinkis

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Past Meetings

Conjugacy classes and related topics

13 Decmber 2013 at the University of Cambridge

  • Description: Conjugacy classes give useful structural information about groups, just how much information the classes, or their sizes, confer is an interesting problem. In this meeting we will look at known results and further questions, both in the finite and infinite setting.

  • Schedule:

    12-1pm Lattices in PSL_2(K), K a local field, Ben Martin

    1-1.45pm - Lunch

    1.45-2.45pm Counting conjugacy classes in some p-adic groups obtained from Chevalley groups, Christopher Voll

    2.45-3.15pm Coffee/Tea

    3.15 - 4.15pm Groups with bounded conjugacy classes, Dan Segal

    4.30-5pm Implications of Conjugacy Class Sizes, Rachel Camina

  • Speakers: Ben Martin (Auckland) , Christopher Voll (Bielefeld), Dan Segal (Oxford), Rachel Camina (Cambridge)

  • Abstracts:

    Lattices in PSL_2(K), K a local field (Ben Martin): Let $K$ be a local field.  I will discuss spaces of conjugacy classes of lattices in $PSL_2(K)$.  Fix a finitely generated group $F$ and let $X(F)$ be the set of conjugacy classes of injective homomorphisms from $F$ to $PSL_2(K)$.  In recent work, Lisa Carbone and I have shown that $X(F)$ can be given the structure of a $K$-analytic manifold, under some hypotheses on $F$.  I will describe some of the ideas underlying this result, including character varieties and automorphism groups of trees.

    Counting conjugacy classes in some p-adic groups obtained from Chevalley groups (Christophr Voll): I will review aspects of the paper “Uniform cell decomposition with applications to Chevalley groups” by Berman, Derakhshan, Onn and Paajanen (JLMS, 2013) concerned with certain zeta functions  associated to groups of rational points of Chevalley groups over local rings. The zeta functions in question count the numbers of conjugacy classes in the congruence quotients of these groups.

    The paper’s main result here is a uniform formula for such conjugacy class zeta functions. It only depends on the Chevalley group and the local ring’s residue field; in particular, it is independent of the ring’s characteristic. I will try and compare this theorem with analogous results and conjectures in representation growth of arithmetic and p-adic analytic groups.

    My exposition will assume no familiarity with the technical machinery used in this paper, viz. p-adic integration and the theory of definable integrals.

    Groups with bounded conjugacy classes (Dan Segal): I will sketch some history, mention some oldish and some more recent results
    about finite groups, and explain how analogous results are obtained for some infinite groups by following the path finite p-groups --> Lie algebras --> pro-p groups.

    Implications of Conjugacy Class Sizes (Rachel Camina): Given the sizes of conjugacy classes of a finite group what can we deduce about the algabraic structure of the group? We will survey various results along this theme.

  • Location: Centre of Mathematical Sciences, Wilberforce Rd, Cambridge.

  • Travel Support : Limited funds are available to reimburse travel expenses of UK-based students and other young mathematicians.

  • Date: 13 December 2013 at 12:00-5:00pm

  • Local Organiser: Rachel Camina

  • Support for the Meeting: The meeting is funded by the LMS Scheme 3 and Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.

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For past meetings during the academic year 2012-13 click here.

For past meetings during the academic year 2011-12 click here.

For past meetings during the academic year 2010-11 click here.

For past meetings during the academic year 2009-10 click here.

For past meetings during the academic year 2008-09 click here.

For past meetings during the academic year 2007-08 click here.

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last significant update 02-Dec-2013
please bring corrections to the attention of Yiftach Barnea
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Complete Calendar of Events

One-Day Meeting: Conjugacy classes and related topics

  • Description: Conjugacy classes give useful structural information about groups, just how much information the classes, or their sizes, infer is an interesting problem. In this meeting we will look at known results and further questions, both in the finite and infinite setting.
  • Speakers: Rachel Camina (Cambridge) or Alan Camina (UEA), Ben Martin (Auckland) , Dan Segal (Oxford), Christopher Voll (Bielefeld).
  • Location: University of Cambridge
  • Date:13 December 2013
  • Local Organiser: Rachel Camina

One-Day Meeting: Mackey Functors for Finite and Infinite Groups

  • Description: TBA
  • Speakers include: Dieter Degrijse (Copenhagen) and Peter Symonds (Manchenster)
  • Location: Royal Holloway, University of London
  • Date: June 2014
  • Local Organiser: Yiftach Barnea and Brita Nucinkis

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Past Meetings

 

Back to Top


For past meetings during the academic year 2012-13 click here.

For past meetings during the academic year 2011-12 click here.

For past meetings during the academic year 2010-11 click here.

For past meetings during the academic year 2009-10 click here.

For past meetings during the academic year 2008-09 click here.

For past meetings during the academic year 2007-08 click here.

Back to Top


last significant update 02-Dec-2013
please bring corrections to the attention of Yiftach Barnea