Invited Speakers

E. Breuillard    
M. Bridson    
G. Fernandez-Alcober    
A. Jaikin-Zapirain    
N. Nikolov    
D. Segal    
A. Shalev    


Workshop on
The Algebraic
Structure of
Profinite Groups

April 7-8, 2008


Department of Mathematics
Royal Holloway
University of London, UK

Yiftach Barnea
Benjamin Klopsch

Email Contact:
profinitegroups at
googlemail dot com

Printable Poster (PDF)
Updated Poster (PDF)
Photos, Lecture Slides etc.

This workshop forms part of the South England Profinite Groups Meetings
which are supported by Scheme 3 of the London Mathematical Society.
The workshop is funded by the EPSRC. We are grateful for the support.

Scope of the Workshop

The focus of the workshop will be on the interplay between the algebraic and the topological properties of profinite groups. In particular, the following two concrete topics will be addressed:

(1) Answering a question which was suggested by J.-P. Serre in the 1960s, N. Nikolov and D. Segal recently proved that in every finitely generated profinite group, every subgroup of finite index is open. An essential concept in this context is verbal width, which was subsequently studied by A. Jaikin-Zapirain in the context of pro-p groups.

(2) Limit groups constitute the class of finitely generated fully residually free groups. Based on earlier work of E. Breuillard, T. Gelander, J. Souto and P. Storm on surface groups, J. Barlev and T. Gelander recently showed that under certain conditions, if a locally compact group G contains a dense free subgroup, then any limit group embeds as a dense subgroup into G. This result applies in particular to profinite groups, and it raises many natural questions. For instance: which finitely generated groups can be embedded as abstract groups into a free pro-p group?

As indicated there are many challenging open problems concerning the algebraic structure of profinite groups. Questions about abstract quotients and subgroups of profinite groups constitute an exciting meeting ground between different areas, including the Theory of Finite Groups, Combinatorial and Geometric Group Theory.

The speakers are encouraged to present key methods and open problems in order to initiate discussions amongst the participants. There will be ample opportunities for informal interactions; for this purpose we will be allowing for long breaks between the talks.

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Invited Talks

The Titles of the invited talks are as follows. Abstracts and supporting material will be made available soon. Speakers are encouraged to present key methods and open problems in order to initiate discussions amongst the participants.

  • Emmanuel Breuillard: Dense subgroups and refinements of the Tits alternative
  • Martin Bridson: Decision problems and profinite completions of groups
    Click here for the three preprints which formed the basis of Martin's talk.
  • Gustavo Fernandez-Alcober: Discrete versus continuous in the (co)homology of pro-p groups
    Click here for the slides (PDF) underlying Gustavo's talk.
  • Andrei Jaikin-Zapirain: On the verbal width of finitely generated pro-p groups
  • Nikolay Nikolov: Strange images of profinite groups
    Click here for notes (PDF) summarising Nikolay's talk.
  • Dan Segal: Words and profinite groups
  • Aner Shalev: Words and Ore's conjecture


Aner Shalev

Gustavo Fernandez-Alcober

Nikolay Nikolov

Emmanuel Breuillard

Jonathan Barlev

Andrei Jaikin-Zapirain

Martin Bridson

Pizza 1

Pizza 2

Pizza 3

Pizza 4
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The online registration was closed on 8 March. In the end we had slightly more people register than we anticipated. We still welcome anybody to express their interest in participating in the workshop by sending us an email. However, we are not likely to be able to cover travel expenses, subsistence or accommodation costs for anybody who registers now (i.e. after 7 March) by email.

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The first lecture of the workshop will start on Monday, 7 April 2008, at 13.00. The last lecture will end on Tuesday, 8 April 2008, at 16.30.

Invited speakers are listed at the top. The titles of their talks are indicated above.

Here are a schedule of talks and a detailed programme (PDF).

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List of Confirmed Participants - as of 7 March 2008 -

Daniel Appel (London, UK), Jonathan Barlev (Cambridge, USA), Yiftach Barnea (London, UK), Mikhail Belolipetsky (Durham, UK), Emmanuel Breuillard (Palaiseau, France), Martin Bridson (Oxford, UK), Christopher Brookes (Cambridge, UK), Jack Button (Cambridge, UK), Rachel Camina (Cambridge, UK), Pierre-Emmanuel Caprace (Bures-sur-Yvette, France), Valentina Colombo (Padova, Italy), Gustavo Fernandez-Alcober (Bilbao, Spain), Lev Glebsky (San Luis Potosi, Mexico), Jon Gonzalez-Sanchez (Santander, Spain), Andrei Jaikin-Zapirain (Madrid, Spain), Gareth Jones (Southampton, UK), Jonathan Kiehlmann (St Andrews, UK), Benjamin Klopsch (London, UK), Charles Leddham-Green (London, UK), Cormac Long (Southampton, UK), John MacQuarrie (Manchester, UK), Nikolay Nikolov (London, UK), Brita Nucinkis (Southampton, UK), Pirita Paajanen (Southampton, UK), Mohan Panchanathan (London, UK), Massimiliano Patassini (Padova, Italy), Martyn Quick (St Andrews, UK), Colin Reid (London, UK), Evija Ribnere (Duesseldorf, Germany), Dan Segal (Oxford, UK), Aner Shalev (Jerusalem, Israel), Simon Turner (Bath, UK), Christopher Voll (Southampton, UK), Thomas Weigel (Milano, Italy), Amaia Zugadi (Bilbao, Spain)

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Practical Information
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last significant update 01.04.2008
please bring corrections to the attention of Benjamin Klopsch