| Katharina Geissler (TU Berlin) | Comp. number theory | 1st Oct 1999 to 30th Sep 2001 | |
| Florian Hess (TU Berlin) | Comp. number theory, Cryptography | 1st Oct 1999 to 30th Nov 2000 | |
| Michael Pohst (TU Berlin) | Number Theory | 30th Jan 2000 to 5th Mar 2000 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 15th Feb 2000 to 19th Feb 2000 | |
| William Stein (Berkeley) | Modular Forms | 1st Apr 2000 to 29th Apr 2000 | |
| Gavin Brown (Oxford) | Algebraic Geometry | 17th Aug 2000 to 16th Aug 2001 | |
| Gregoire Lecerf (École Polytechnique, Paris) | Commutative Algebra | 17th Aug 2000 to 15th Sep 2000 | |
| Stefi Cavallar (CWI, Amsterdam) | Comp. number theory | 20th Oct 2000 to 6th Nov 2000 | |
| Eamonn O'Brien (Auckland) | Comp. group theory | 1st Nov 2000 to 30th Nov 2000 | |
| Arjeh Cohen (UT, Eindhoven) | Lie Theory | 5th Nov 2000 to 31st Dec 2000 | |
| David Bayer (Columbia) | Algebraic Geometry | 10th Dec 2000 to 15th Jan 2001 | |
| Miles Reid (Warwick) | Algebraic Geometry | 14th Dec 2000 to 15th Jan 2001 | |
| Pierrick Gaudry (École Polytechnique, Paris) | Comp. number theory | 6th Jan 2001 to 24th Mar 2001 | |
| Sebastian Pauli (Concordia Montreal) | Comp. number theory | 11th Jan 2001 to 1st Mar 2001 | |
| Josef Schicho (Linz) | Algebraic Geometry | 1st Feb 2001 to 28th Feb 2001 | |
| Bettina Eick (Kassel) | Comp. group theory | 22nd Feb 2001 to 11th Mar 2001 | |
| Dimitri Leemans (Bruxelles Libre) | Group Theory, Incidence Geometry | 1st Apr 2001 to 5th May 2001 | |
| Helena Verrill (Copenhagen) | Algebraic Geometry | 30th Apr 2001 to 28th May 2001 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 7th May 2001 to 25th May 2001 | |
| William Stein (Harvard) | Modular Forms | 8th May 2001 to 31st May 2001 | |
| Graham Norton (UQ) | Coding Theory | 28th May 2001 to 9th Jun 2001 | |
| Miles Reid (Warwick) | Algebraic Geometry | 16th Jul 2001 to 10th Aug 2001 | |
| Willem de Graaf (Utrecht) | Lie Theory | 1st Aug 2001 to 21st Aug 2001 | |
| Axel Kohnert (Bayreuth) | Combinatorics | 12th Aug 2001 to 2nd Apr 2002 | |
| Jürgen Klüners (IWR Heildelberg) | Number Theory | 29th Aug 2001 to 12th Oct 2001 | |
| Scott McCullum (Maquarie, Sydney) | Commutative Algebra | 15th Oct 2001 to 30th Jun 2002 | |
| Paul Zimmermann (INRIA France) | Comp. number theory | 29th Oct 2001 to 11th Nov 2001 | |
| Emmanuel Thome (U. P et M Curie, Paris) | Comp. number theory, Cryptography | 1st Nov 2001 to 9th Dec 2001 | |
| Martine Girard (Leiden) | Arithmetic Geometry | 3rd Nov 2001 to 26th Nov 2001 | |
| Colva Roney-Dougal (QMUL) | Comp. group theory | 29th Nov 2001 to 28th Nov 2002 | |
| Pierrick Gaudry (École Polytechnique, Paris) | Comp. number theory | 1st Dec 2001 to 7th Dec 2001 | |
| Csaba Schneider (UWA) | Group Theory | 1st Dec 2001 to 15th Dec 2001 | |
| Dimitri Leemans (Bruxelles Libre) | Group Theory, Incidence Geometry | 1st Jan 2002 to 31st Jan 2002 | |
| Wieb Bosma (Nijmegen) | Comp. number theory | 22nd Jan 2002 to 15th Jul 2002 | |
| David Glynn (Royal Society, NZ) | Coding Theory, Finite Geometry | 29th Jan 2002 to 28th Jan 2003 | |
| Helena Verrill (Hanover) | Algebraic Geometry | 8th Feb 2002 to 7th Mar 2002 | |
| Bettina Eick (Braunschweig) | Comp. group theory | 24th Feb 2002 to 23rd Mar 2002 | |
| Eamonn O'Brien (Auckland) | Comp. group theory | 24th Feb 2002 to 2nd Mar 2002 | |
| Markus Grassl (Karlsruhe) | Coding Theory, Quamtum Computing | 8th Mar 2002 to 10th Apr 2002 | |
| Paul van Wamelen (LSU Baton Rouge) | Arithmetic Geometry | 1st Jun 2002 to 31st Jul 2003 | |
| Andreas Enge (École Polytechnique, Paris) | Comp. number theory | 24th Jun 2002 to 12th Jul 2002 | |
| Laura C. Gaardsted (Aarhus) | Comp. number theory | 1st Sep 2002 to 31st Dec 2002 | |
| Robert Wilson (Birmingham) | Representation Theory | 1st Sep 2002 to 14th Oct 2002 | |
| Derek Holt (Warwick) | Group Theory | 19th Oct 2002 to 13th Dec 2002 | |
| Colva Roney-Dougal (QMUL) | Comp. group theory | 29th Nov 2002 to 28th Nov 2003 | |
| Pierrick Gaudry (École Polytechnique, Paris) | Comp. number theory | 7th Dec 2002 to 15th Dec 2002 | |
| George Havas (UQ) | Comp. group theory | 9th Dec 2002 to 16th Dec 2002 | |
| Alexa van der Waall (Simon Fraser) | Differential Algebra | 2nd Jan 2003 to 31st Dec 2003 | |
| Michael Monagan (Simon Fraser) | Computational Algebra | 13th Jan 2003 to 1st Jul 2003 | |
| Eamonn O'Brien (Auckland) | Comp. group theory | 21st Jan 2003 to 15th Feb 2003 | |
| Martin Bright (Liverpool) | Arithmetic Geometry | 23rd Jan 2003 to 21st Apr 2003 | |
| Victor Flynn (Liverpool) | Arithmetic Geometry | 23rd Jan 2003 to 25th Apr 2003 | |
| Sebastian Pauli (TU Berlin) | Comp. number theory | 3rd Mar 2003 to 4th Apr 2003 | |
| Mark Watkins (Penn State U) | Analytic Number Theory | 15th May 2003 to 15th Aug 2003 | |
| William Stein (Harvard) | Modular Forms | 2nd Jun 2003 to 30th Jun 2003 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 6th Jul 2003 to 13th Jul 2003 | |
| George Havas (UQ) | Comp. group theory | 16th Jul 2003 to 23rd Jul 2003 | |
| Tom Womack (Nottingham) | Comp. number theory | 23rd Jul 2003 to 10th Sep 2003 | |
| Gavin Brown (Warwick) | Algebraic Geometry | 9th Aug 2003 to 31st Oct 2003 | |
| Michael Pohst (TU Berlin) | Number Theory | 9th Oct 2003 to 9th Nov 2003 | |
| Volker Weispfenning (Passau) | Computer Algebra | 15th Nov 2003 to 24th Nov 2003 | |
| Eamonn O'Brien (Auckland) | Comp. group theory | 18th Jan 2004 to 24th Jan 2004 | |
| Willem de Graaf (Utrecht) | Lie Theory | 1st Feb 2004 to 30th Sep 2004 | |
| Markus Grassl (Karlsruhe) | Coding Theory, Quamtum Computing | 14th Feb 2004 to 20th Mar 2004 | |
| John Bray (Birmingham) | Group Theory | 10th Mar 2004 to 2nd Apr 2004 | |
| Mark Watkins (Penn State U) | Analytic Number Theory | 1st Jul 2004 to 31st May 2005 | |
| Dan Bernstein (Illinois) | Comp. number theory, Cryptography | 16th Jul 2004 to 14th Aug 2004 | |
| Sergei Haller (Giessen) | Comp. group theory | 18th Aug 2004 to 25th Sep 2004 | |
| Janka Pilnikova (RISC, Linz) | Algebraic Geometry | 28th Aug 2004 to 27th Sep 2004 | |
| Robert Fraatz (TU. Berlin) | Comp. number theory | 1st Oct 2004 to 31st Dec 2004 | |
| Alexa van der Waall (Simon Fraser) | Differential Algebra | 1st Oct 2004 to 30th Apr 2005 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 13th Oct 2004 to 13th Nov 2004 | |
| Tim Dokchitser (Durham) | L-Functions | 25th Oct 2004 to 4th Dec 2004 | |
| Gavin Brown (Warwick) | Algebraic Geometry | 21st Nov 2004 to 31st Dec 2004 | |
| Nils Bruin (Simon Fraser) | Number Theory | 20th Dec 2004 to 28th Feb 2005 |