South England Profinite Groups Meetings

Asymptotic Group Theory and Model Theory

26-27 March 2012 at Royal Holloway University of London

• Description: Over the last thirty years model-theoretic constructions and techniques have had a significant impact in areas such as number theory, algebraic geometry and group theory. Important roles are played, for instance, by various limit constructions and methods from p-adic and motivic integration.
  In the workshop we will survey some of the current trends at the interface of model theory and group theory. With a view towards applications in asymptotic and geometric group theory, the workshop will focus on three broad topics: (1) Approxiamte groups and Gromov's Polynomial Growth Theorem, (2) Limit groups, group equations and related topics, (3) Motivic and p-adic integration with applications to groups.
• Local Organiser: Benjamin Klopsch
• Further Details: Workshop Webpage

One-Day Meeting: Profinite Completions of Groups

• Description: Every residually finite group embeds as a dense subgroup into its profinite completion, and the profinite completion construction is an important tool in studying infinite groups. There are many interesting open questions about the relationship between abstract groups, their profinite completions and profinite groups in general.
• Speakers: M. Aka (Hebrew University of Jerusalem), D. Segal (University of Oxford), H. Wilton (University College London)
• Location: Imperial College London
• Date: 12 December 2011
• Local Organiser: Nikolay Nikolov

Two-Day Workshop: Asymptotic Group Theory and Model Theory

• Description: Over the last thirty years model-theoretic constructions and techniques have had a significant impact in areas such as number theory, algebraic geometry and group theory. Important roles are played, for instance, by various limit constructions and methods from p-adic and motivic integration.
  In the workshop we will survey some of the current trends at the interface of model theory and group theory. With a view towards applications in asymptotic and geometric group theory, the workshop will focus on three broad topics: (1) Approxiamte groups and Gromov's Polynomial Growth Theorem, (2) Limit groups, group equations and related topics, (3) Motivic and p-adic integration with applications to groups.
• Speakers: R. Cluckers (Université Lille and K. U. Leuven), H. Helfgott (CNRS/Ecole Normale Supérieure Paris), J. Howie (Heriot-Watt University, Edinburgh), I. Kazachkov (University of Oxford), F. Loeser (Université Pierre et Marie Curie, Paris), H. D. Macpherson (University of Leeds), U. Onn (Ben Gurion University of the Negev), A. Ould Houcine (Universités de Lyon and de Mons)
• Location: Royal Holloway, University of London
• Date: 26-27 March 2012
• Local Organiser: Benjamin Klopsch
• Further Details: Workshop Webpage

One-Day Meeting: Hausdorff Dimension in Profinite Groups

• Description: The aim of the meeting will be to explore, in a range of settings, Hausdorff dimension arguments in the theory of profinite groups.
• Speakers (tbc): M. Abert (Alfréd Rényi Institute of Mathematics, Budapest), Y. Barnea (Royal Holloway University of London), R. Camina (University of Cambridge), B. Klopsch (Royal Holloway University of London)
• Location: University of Southampton
• Date: 22 June 2012
• Local Organiser: Martin Kassabov
• Further Details: will be posted in due course

Profinite Completions of Groups

12 December 2011 at Imperial College London

• Description: The meeting will be centered around profinite completions. Every residually finite group embeds as a dense subgroup into its profinite completion, and the profinite completion construction is an important tool in studying infinite groups. There are many interesting open questions about the relationship between abstract groups, their profinite completions and profinite groups in general. The natural problem `Which profinite groups are completions of finitely generated groups?' seems impossibly hard.

  There will be three talks and one problem session with breaks for discussions. The programme will start at 13:00 and it will end at 18:00. The precise programme is as follows.

  13.00 - 14.00   Sandwich Lunch
  14.00 - 15.00   Profinite completions (Dan Segal)
  15.00 - 15.30   Coffee break
  15.30 - 16.30   Arithmetic groups with isomorphis finite quotients (Menny Aka)
  16.45 - 17.45   The triviality problem for profinite completions of finitely presented groups (Henry Wilton)
  17.45 - 18.00   Open Problems (Menny Aka, Dan Segal, Henry Wilton et al.)

• Location: Imperial College London
• Date: Monday, 12 December 2011
• Local Organiser: Nikolay Nikolov
• Further Information: The precise venue is: Room 341 in the Department of Mathematics, 180 Queen's Gate, Imperial College London, SW7 2AZ. Contact the local organiser if you need travel directions or require further information.