South England Profinite Groups Meetings

The series of meetings has finished. We are planning to start a new series of events in December 2011. Many thanks to all participants!

One-Day Meeting: Hereditarily Just Infinite Groups

• Description: The classification of finite simple groups is one of the greatest achievements of 20th century mathematics. In the category of profinite (or subcategory of pro-p groups), the `simple' objects are the so-called just infinite groups. Loosely speaking, the study of these groups reduces to the study of branch groups and hereditarily just-infinite groups. The meeting will focus on what is known about the latter type, with particular emphasis on novel constructions of J.S. Wilson and of M. Ershov and A. Jaikin-Zapirain.
• Location: Royal Holloway, University of London
• Date: 17 December 2010
• Local Organiser: Benjamin Klopsch

One-Day Meeting: The McKay and the Broué conjectures

• Description: Much of the recent work in the representation theory of finite groups has centered around the fundamental abelian defect group conjecture of Broué, and a web of related conjectures, notably the McKay conjecture. An underlying idea of these conjectures is that certain aspects of the representation theory of a finite group should be determined `locally', that is, by the representation theory of so-called local subgroups (e.g., the normalisers of p-Sylow subgroups).
• Location: University of Southampton
• Date: Tuesday, 12 April 2011
• Local Organiser: Alexander Stasinski
• Further Information: Further details can be found at the meeting's web page.

One-Day Meeting: Iwasawa Algebras

• Description: Non-commutative Iwasawa algebras form a large and interesting class of Noetherian algebras. They are constructed as completed group algebras of compact p-adic analytic groups. They were first defined and many of their fundamental properties were derived by M. Lazard in 1965. Interest in them has been revived by developments in number theory over the past twenty years.
• Location: University if Cambridge
• Date: Tuesday, 21 June 2011
• Local Organiser: Rachel Camina
• Further Details: Further details can be found at the meeting's web page.

Hereditarily Just Infinite Groups

17 December 2010 at Royal Holloway (University of London)

• Description: The classification of finite simple groups is one of the greatest achievements of 20th century mathematics. In the category of profinite (or subcategory of pro-p groups), the `simple' objects are the so-called just infinite groups. Loosely speaking, the study of these groups reduces to the study of branch groups and hereditarily just-infinite groups. The meeting will focus on what is known about the latter type, with particular emphasis on novel constructions of J.S. Wilson and of M. Ershov and A. Jaikin-Zapirain.

  There will be three talks and one problem session with breaks for discussions. The programme will start at about 11:45 and it will end at about 17:15. A tentative schedule is as follows. Click here for a printable programme and here for a printable poster.

  12.00 - 13.00   Hereditarily just infinite groups - a brief introduction (Benjamin Klopsch)
  13.00 - 14.00   Sandwich Lunch
  14.00 - 15.00   Large hereditarily just infinite groups (John Wilson)
  15.30 - 16.30   Quantifying the (hereditary) just infinite property (Colin Reid)
  16.45 - 17.00   Open Problems (Yiftach Barnea et al.)

• Location: Royal Holloway, University of London, McCrea Building, Room 336
• Date: Friday, 17 December 2010
• Local Organiser: Benjamin Klopsch
• Practical Information: The meeting will take place in the McCrea Building, Room 336. For a Campus plan, other maps and travel directions start from the College's Visitor Information.
  Please send a short email to profinitegroups@googlemail.com if you intend to come so that we can make adequate provisions for lunch and tea.
• Resources:
  Y. Barnea, N. Gavioli, A. Jaikin-Zapirain, V. Monti, C. M. Scoppola: Pro-p groups with few normal subgroups, J. Algebra 321 (2009); see here.
  M. Ershov, A. Jaikin-Zapirain: Groups of positive weighted deficiency and their applications, arXiv:1007.1489, available here.
  C. Reid: On the structure of just infinite profinite groups, arXiv:0906.1771v2, available here.
  C. Reid: Subgroups of finite index and the just infinite property, arXiv:0905.1624v1, available here.
  C. Reid: On (hereditarily) just infinite profinite groups that are not virtually pro-p, arXiv:1010.3979v1, available here.
  J.S. Wilson, On abstract and profinite just-infinite groups, in: New Horizons in Pro-p Groups, Birkhäuser, 2000; see here.
  J.S. Wilson, Large hereditarily just infinite groups, J. Algebra 324 (2010); see here.
  Please contact the local organiser if you want further suggestions to be included.

The McKay and the Broué conjectures

12 April 2011 at the University of Southampton

• Description: Much of the recent work in the representation theory of finite groups has centered around the fundamental abelian defect group conjecture of Broué, and a web of related conjectures, notably the McKay conjecture. An underlying idea of these conjectures is that certain aspects of the representation theory of a finite group should be determined `locally', that is, by the representation theory of so-called local subgroups (e.g., the normalisers of p-Sylow subgroups).

• Location: University of Southampton
• Date: Tuesday, 12 April 2011
• Local Organiser: Alexander Stasinski
• Further Information: Further details can be found at the meeting's web page.

Iwasawa Algebras

21 June 2011 at the University of Cambridge

• Description: Non-commutative Iwasawa algebras form a large and interesting class of Noetherian algebras. They are constructed as completed group algebras of compact p-adic analytic groups. They were first defined and many of their fundamental properties were derived by M. Lazard in 1965. Interest in them has been revived by developments in number theory over the past twenty years.

• Location: University of Cambridge
• Date: Tuesday, 21 June 2011
• Local Organiser: Rachel Camina
• Further Information: Further details can be found at the meeting's web page.