Computational Algebra Group

Computational Algebra Group

The basic mission of the Computational Algebra Group is the development of computer techniques for solving symbolic problems in mathematics, with particular emphasis on the areas of algebra, number theory and geometry. The activities extend from the design of algorithms through to the construction of computer algebra packages and languages. The group concentrates on what might be called discrete algebraic and combinatorial structures: groups, rings, fields, modules, algebras, designs and geometries. A particular strength of the group is its expertise in computational methods across several major branches of mathematics.

The Computational Algebra Group provides a unique environment in that it brings together mathematicians, computer scientists and software engineers. The development of good algorithms requires the involvement of leading researchers from the relevant areas of mathematics. The efficient implementation and embedding of these algorithms in large integrated software systems requires sophisticated techniques from computer science. The design and implementation of algebraic programming languages requires the involvement of both mathematicians and computer scientists.

The group holds a regular Computational Algebra Seminar, and hosts approximately twenty visitors each year. The Computational Algebra Group also distributes the computer algebra system Magma, which has been cited in approximately 4000 research publications.

Current Members

Professors

Senior Research Fellows

Research Fellows

Administrative Officer

Honorary Research Associates

Historical Members

All members of the Computational Algebra Group from 2000 to present.

Alexa van der Waall
  • Member (2003)
Alexander Kasprzyk
  • Research Fellow (2009–2010) From Nov 1
Alexandra Flynn
  • Member (1995–1998)
Ali Mohammadi
  • PhD Student (2012–2018)
Allan Steel
  • Member (1989–1999)
  • Software Engineer (2000)
  • PhD Student (2001–2011) P/T
  • Research Fellow (2001–2009)
  • Senior Research Fellow (2010–2025)
Andreas Previtali
  • Visiting Scientist (2007–2008) From 1 Oct; To Feb 28
Andreas-Stephan Elsenhans
  • Research Fellow (2012–2015) From November 1; To March 2015
Anne Cannon
  • Administrative Officer (2000–2025)
Arjen Lenstra
  • Honorary Research Associate (2000–2008)
Ben Smith
  • Member (2000–2001)
  • Software Engineer (2002)
  • Member (2003)
Bernd Souvignier
  • Member (1996–1997)
Bill Unger
  • Member (1998–1999)
  • Research Fellow (2000–2009)
  • Senior Research Fellow (2010–2025)
Brendan Creutz
  • Research Associate (2011) From April 1
  • (2012)
  • Research Associate (2013) To October 11
Bruce Cox
  • Member (1990–1998)
  • Software Engineer (2000–2003) To Aug 31
Catherine Playoust
  • Member (1989–1996)
Chris Reid
  • MSc Student (2008)
  • MSc Student (2010)
Claus Fieker
  • Postdoc (2000–2001) From April 1
  • Research Fellow (2002–2007)
  • Senior Research Fellow (2008–2011)
  • Honorary Research Associate (2012–2025)
Colva M. Roney-Dougal
  • Member (2001–2003)
Damien Fisher
  • Software Engineer (2000–2006) To July 30
Damien Stehl{é
  • Member (2006)
  • Member (2008–2010)
Damien Stehlé
  • Postdoc (2006)
  • Visiting Scientist (2008–2010) ENS, Lyon, From July 1; ENS, Lyon
Dan Roozemond
  • Postdoc (2006) From 1 May
  • Research Fellow (2010–2012) From May 1; To March 31
David Howden
  • Research Associate (2012–2014) From July 8; To July 2014
David Kohel
  • Member (1999)
  • Research Fellow (2000–2001)
  • Member (2002)
Don Taylor
  • Senior Research Fellow (2010–2025)
Edgar Costa
  • Research Fellow (2024–2025)
Emanuel Herrmann
  • Member (1999)
Eran Assaf
  • Research Fellow (2024–2025)
Florian Hess
  • Postdoc (2000)
Florian Heß
  • Member (1999–2001)
Fre Vercauteren
  • Postdoc (2006–2007) From 1 Sept; To Feb 28
Gareth White
  • PhD Student (2008–2015)
Gavin Brown
  • Member (1998–1999)
  • Postdoc (2000)
  • Member (2001)
Geoff Bailey
  • Member (1995–1999)
  • Research Associate (2000–2009)
  • Research Fellow (2010–2025)
Graham Matthews
  • Member (1989–1993)
Greg White
  • Member (2000–2001)
  • Software Engineer (2002–2006)
  • PhD Student (2003–2006)
Hamish Ivy Law
  • PhD Student (2008–2012) Cotuelle
Herbert Brückner
  • Member (1998–1999)
Ivan Morel
  • PhD Student (2008–2011) Cotuelle
Jasper Scholten
  • Postdoc (2005–2007) From 1 Dec
Jean-François Biasse
  • Postdoc (2010–2011) From Oct 14; to Mar 14
John Cannon
  • Member (1971–1999)
  • Professor and Head (2000–2023)
  • Professor (2024–2025)
John Voight
  • Member (2005–2006)
  • Professor (2024–2025)
Katharina Geissler
  • PhD Student (2000) TU, Berlin
Katharina Geiß ler
  • Member (1999–2001)
Ley Wilson
  • PhD Student (2008–2010)
Makoto Suwama
  • PhD Student (2015)
Mark Watkins
  • Member (2003)
  • Postdoc (2004–2005) From July 1; To June 30
  • Research Fellow (2008–2023) From July 1
  • Honorary Research Associate (2024–2025)
Markus Kirschmer
  • Postdoc (2009–2010) From 1 Oct
Michael Gleeson
  • Administrative Officer (2009–2013) From Sept 1; To November 29
Michael Harrison
  • Postdoc (2003–2005) From July 1; To June 30
  • Research Fellow (2005–2015) From July 1; To May 2015
  • Research Fellow (2018–2020)
Michael Slattery
  • Member (1987–2006)
Nicole Sutherland
  • Member (1999)
  • Software Engineer (2000–2023)
  • PhD Student (2008–2015) P/T; P/T to April 2015
  • Research Fellow (2024–2025)
Nils Bruin
  • Research Fellow (2002–2003) From Sept 1; To Sept 30
Paul B. van Wamelen
  • Member (2002–2003)
Paulette Lieby
  • Member (1999)
  • Software Engineer (2000)
  • Research Associate (2001–2003)
Richard Rannard
  • Member (1997–1998)
Scott Contini
  • Research Fellow (2000–2001) To Feb 1
Scott Murray
  • Postdoc (2000–2007) From Sept 9; USYD Post-doc, To July 31
  • Research Fellow (2007–2009) From Aug 1
  • Honorary Research Associate (2010–2018)
Sergei Haller
  • Member (2004)
  • Postdoc (2006–2007) To May 15
Stephan Elsenhans
  • Senior Research Fellow (2024–2025)
Steve Donnelly
  • Research Fellow (2005–2017) From Nov 1
Volker Gebhardt
  • Member (1999)
  • Postdoc (2000–2001) To Aug 31
  • Research Fellow (2001–2003) From Sept 1; To Sept 1
  • Honorary Research Associate (2003–2025)
Wieb Bosma
  • Member (1989–1996)
Willem de Graaf
  • Postdoc (2004)
  • Member (2005)
Yinan Zhang
  • PhD Student (2009–2015)