South England Profinite Groups Meetings

Joint Research Group funded by LMS Scheme 3
Academic Year 2008-09

This page keeps record of the meetings held during the year 2008-09.
Please click here to move to events scheduled for this year.

Background: In recent years profinite and asymptotic methods have been successfully applied to general problems of group theory. In addition there are interesting links to number theory and geometry.
Activities: During the academic year 2008-09 we are holding a series of three 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.
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.
Organisers: Corresponding organisers of the Joint Research Group are Benjamin Klopsch (Royal Holloway, University of London), Nikolay Nikolov (Imperial College London) and Christopher Voll (University of Southampton).

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There will be no more meetings this year. But we will apply for a renewal of the grant over the summer so that we can organise a similar series of meetings during the academic year 2009-10.
If you have any comments regarding past meetings or suggestions regarding future meetings, please let us know.

Many thanks to all participants and local organisers for making this series of events so successful!

Complete Calendar of Events

One-Day Meeting: Kac-Moody Groups - a Profinite Perspective

Description: The meeting will introduce newcomers to Kac Moody algebras and groups. It will then move on to recent results and open problems from a profinite perspective.
Location: Royal Holloway, University of London
Date: 17 December 2008
Local Organisers: Yiftach Barnea and Benjamin Klopsch

Two-Day Workshop: Representations and Asymptotic Group Theory

Description: The workshop will bring together people with interests in asymptotic and arithmetic aspects of the representation theory of infinite groups or families of finite groups. A guiding theme will be representation growth, e.g. in arithmetic and p-adic Lie groups. Related topics include: representations of finite reductive groups, smooth representations of locally-compact p-adic Lie groups in the context of the Langlands conjectures and conjugacy classes in finite p-groups.
Location: University of Southampton
Date: 6-7 April 2009
Local Organiser: Christopher Voll, in co-operation with Benjamin Klopsch
Further Details: Workshop Webpage

One-Day Meeting: Rank Gradient of Groups

Description: We will introduce the concept of rank gradient and explain its connections to measurable group actions, L²-Betti numbers and hyperbolic 3-manifold theory.
Location: Imperial College London
Date: 12 June 2009
Local Organiser: Nikolay Nikolov
Resources: Preprint on "The rank gradient from a combinatorial viewpoint" and Preprint on "Rank gradient, cost of groups and the rank versus Heegaard genus problem".

Past Meetings

Kac-Moody Groups - a Profinite Perspective

17 December 2008 at Royal Holloway (University of London)

Description: The meeting will introduce newcomers to Kac-Moody algebras and groups. It will then move on to recent results and open problems from a profinite perspective.
There will be three talks and one problem session with breaks for discussions. The programme will start at about 11:30 and it will end at about 17:15. Click here for a printable programme.
12.00 - 13.00 Introductory talk (Christopher Voll)
14.00 - 15.00 Kac-Moody groups with property T: Ershov's construction (Nikolay Nikolov)
15.30 - 16.30 Rank rigidity for lattices in products of Kac-Moody groups (Pierre-Emmanuel Caprace)
16.45 - 17.00 Open Problems (Pierre-Emmanuel Caprace et al.)
Location: Royal Holloway, University of London
Date: Wednesday, 17 December 2008
Local Organisers: Yiftach Barnea and Benjamin Klopsch
Practical Information: The meeting will take place in the McCrea Building, Room 219. For a Campus plan, other maps and travel directions follow the respective link from the College's Visitor Guide. The organisers would appreciate if you could register your intention to participate by sending a short email to profinitegroups at googlemail dot com. This is also the preferred email address for all inquiries regarding this meeting.
Resources: K. Brown: Introduction to Kac-Moody groups and twin buildings, 1999, available here.
P.-E. Caprace and B. Remy, Groups with a root group datum, 2008, available here.
M. Ershov, Golod-Shafarevich groups with property (T) and Kac-Moody groups, to appear in Duke Math. J., preprint available here.
V. Kac, Infinite-Dimensional Lie Algebras, 1994, preview at google books.
R. V. Moody and A. Pianzola, Lie Algebras with Triangular Decompositions, 1995, preview at google books.
Open Problems Handout: A short list prepared by Pierre-Emmanuel Caprace and distributed during the meeting.

Representations and Asymptotic Group Theory

6-7 April 2009 at the University of Southampton

Description: The workshop will bring together people with interests in asymptotic and arithmetic aspects of the representation theory of infinite groups or families of finite groups. A guiding theme will be representation growth, e.g. in arithmetic and p-adic Lie groups. Related topics include: representations of finite reductive groups, smooth representations of locally-compact p-adic Lie groups in the context of the Langlands conjectures and conjugacy classes in finite p-groups.
Location: University of Southampton
Date: 6-7 April 2009
Local Organiser: Christopher Voll, in co-operation with Benjamin Klopsch
Further Information: Please visit the Workshop Web Page.

Rank Gradient of Groups

12 June 2009 at Imperial College London

Description: The concept of rank gradient was first introduced by Marc Lackenby for the study of hyperbolic 3 manifolds and later shown to have connections with several seemingly disjoint areas of mathematics: group theory, measurable group actions, L²-Betti numbers and entropy.
The meeting will be introductory in nature and we will indicate the main open problems and directions still to be explored in this area. There will be three talks and one problem session with breaks for discussions. The programme will start at about 12:00 and it will end at about 17:00. The preliminary schedule of talks is as follows.
12.00 - 13.00 The Cost of Profinite Actions (Nikolay Nikolov)
14.00 - 15.00 A p-Group of Positive Rank Gradient (Jan-Christoph Schlage-Puchta)
15.30 - 16.30 Rank Gradient, Property Tau and Hyperbolic 3-Manifolds (Marc Lackenby)
16.45 - 17.00 Open Problems
Location: Imperial College London
Date: Friday, 12 June 2009
Local Organiser: Nikolay Nikolov
Practical Information: Please contact the local organiser by email if you intend to come. The venue is Huxley 140 in the Department of Mathematics at Imperial College London. Instruction how to reach Imperial College can be found here. Lunch and coffee/tea will be provided for the number of participants registered.
Resources: Some relevant references are:
M. Lackenby, Expanders, rank and graphs of groups Israel J. Math. 146 (2005) 357-370, ps file.
M. Abert, N. Nikolov, Rank gradient, cost of groups and the rank versus Heegaard genus problem, arXiv preprint.

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

last significant update 18.08.2009
please bring corrections to the attention of Benjamin Klopsch