Royal Holloway University Of London

Algebra Group

Members of the Algebra Group at Royal Holloway are interested in various aspects of Group Theory and its relations to other subject areas. Our main research areas include: Asymptotic Group Theory, Lie Groups and Lie Algebras, Combinatorial Aspects of Groups, Profinite Groups, and Application of Algebra to Cryptography. We work in collaboration with other research groups within the department such as the Information Security and Cryptography Group, the Number Theory Group and the Discrete Mathematics and its Applications Group. More details about the specific research interests of individual members of the Algebra Group can be found on the corresponding personal web pages.

The Algebra Group maintains a lively research atmosphere, fostered by internationally renowned visitors. The weekly research seminars in Pure Mathematics and in Information Security, which regularly feature talks in Algebra, are supplemented by informal Reading Seminars or Advanced Classes. Members of the Algebra Group at Royal Holloway also participate in the inter-collegial London Algebra Colloquium. With their colleagues in Cambridge, London and Southampton they organise the South England Profinite Groups Meetings, which are supported by the London Mathematical Society.

Applicants for postgraduate studies are very welcome. Please contact any member of the group for further details, and see the departmental web page on Ph.D. Research for formal arrangements and scholarship opportunities. Current research students in the Algebra Group benefit from a range of high level courses in various subjects, taught at the LTCC.

Group Members

  • Dr. Yiftach Barnea (Asymptotic Group Theory, Profinite Groups and Lie Algebras) 
  • Prof. Simon Blackburn (Combinatorial Aspects of Groups and Application of Algebra to Cryptography)
  • Dr. Benjamin Klopsch (Asymptotic Group Theory: Subgroups and Representations, Profinite Groups, e.g. infinite Galois groups; Lie theory; Arithmetic groups; connections with Number Theory and Combinatorics)
  • Dr. Mark Wildon (Representation Theory of Symmetric Groups and related algebras; connections with Group Theory and Combinatorics)

Current Research Students

  • Liaqat Ali (Topic: Representation Zeta Functions of Groups, Dr. Klopsch)
  • Daniel Appel (Topic: Automorphism Groups of Free Groups, Dr. Klopsch)
  • Sarah Middleton (Group Theory, Dr. Barnea)
  • Ciaran Mullan (Algebraic Methods in Cryptography, Prof. Blackburn and Dr. Cid)
  • Theofanis Alexoudas (Group Theory, Dr. Klopsch)
  • Eugenio Giannelli (Representation theory, Dr. Wildon)

Recent, Current and Future Visitors

  • Dr. C. Roever (National University of Ireland, Galway), July 2009
  • Prof. M. Ershov (University of Virginia, Charlottesville), June 2009
  • Dr. J. Gonzalez-Sanzchez (University of Santander), April-August 2009
  • Dr. M. Berman (University of the Negev), March 2009
  • Prof. N. Boston (University of Wisconsin, Madison and University College Dublin), November 2008
  • Prof. A. Jaikin-Zapirain (Universidad Autónoma de Madrid), April 2008
  • Prof. O. Baues (Universitaet Karlsruhe), March 2007
  • Prof. T. Weigel (Univesitá degli Studi di Milano-Bicocca), February 2006
  • Prof. D. S. Passman (University of Wisconsin, Madison), September 2005

Conferences and Meetings at Royal Holloway

Dr. Barnea and Dr. Klopsch are co-organisers of the South England Profinite Groups Meetings. The following meetings at Royal Holloway form part of the continuing program:

  • Just Infinite Profinite Branch Groups, 12 December 2009
  • Kac-Moody Groups - a Profinite Perspective, 17 December 2008
  • The Algebraic Structure of Profinite Groups, 7-8 April 2008

Dr. Wildon organised a one-day meeting on The Symmetric Groups: Representations and Combinatorics, held at Royal Holloway on 29 March 2011.

Other Activities, News, etc.

Nuffield Science Bursaries Undergraduate Research.  We support strong undergraduate students to carry out small research projects under the Nuffield scheme. In 2009 Tom Smith and Dr. Klopsch are studying Diameters of certain Orbital Graphs.