| Mark Watkins (Penn State U) | Analytic Number Theory | 1st Jul 2004 to 31st May 2005 | |
| Alexa van der Waall (Simon Fraser) | Differential Algebra | 1st Oct 2004 to 30th Apr 2005 | |
| Nils Bruin (Simon Fraser) | Number Theory | 20th Dec 2004 to 28th Feb 2005 | |
| Colva Roney-Dougal (St. Andrews) | Geometric Topology | 21st Jan 2005 to 13th Feb 2005 | |
| Amnon Rosenmann (Ben-Gurion) | Group Theory | 1st Feb 2005 to 28th Feb 2005 | |
| Arjeh Cohen (UT, Eindhoven) | Lie Theory | 19th Feb 2005 to 4th Mar 2005 | |
| Mark Stather (Warwick) | Comp. group theory | 19th Feb 2005 to 13th Mar 2005 | |
| Florian Hess (TU Berlin) | Comp. number theory, Cryptography | 28th Feb 2005 to 10th Apr 2005 | |
| Steven Galbraith (Royal Holloway) | Cryptograohy | 12th Mar 2005 to 14th Mar 2005 | |
| Derek Holt (Warwick) | Group Theory | 19th Mar 2005 to 16th Apr 2005 | |
| Sebastian Pauli (TU Berlin) | Comp. number theory | 24th Mar 2005 to 6th May 2005 | |
| David Glynn (Royal Society, NZ) | Coding Theory, Finite Geometry | 29th Mar 2005 to 25th Apr 2005 | |
| Paul Zimmermann (INRIA France) | Comp. number theory | 14th Apr 2005 to 3rd May 2005 | |
| Oliver Goodman (University of Melbourne) | Topology | 12th May 2005 to 13th May 2005 | |
| Willem de Graaf (Trento) | Lie Theory | 5th Jun 2005 to 28th Jun 2005 | |
| Miles Reid (Warwick) | Algebraic Geometry | 1st Sep 2005 to 14th Sep 2005 | |
| Frank Schreyer (Saarbrucken) | Algebraic Geometry | 1st Sep 2005 to 1st Oct 2005 | |
| John Voight (Berkeley) | Arithmetic Geometry | 1st Sep 2005 to 31st Aug 2006 | |
| Robert Wilson (Birmingham) | Representation Theory | 24th Sep 2005 to 12th Oct 2005 | |
| Jasper Scholten (Leuven) | Arithmetic Geometry | 1st Dec 2005 to 28th Feb 2006 | |
| James Hirschfield (Sussex) | Finite Geometry | 9th Dec 2005 to 5th Jan 2006 | |
| Sergei Haller (Giessen) | Comp. group theory | 11th Jan 2006 to 10th Oct 2006 | |
| Wieb Bosma (Nijmegen) | Comp. number theory | 15th Jan 2006 to 31st Jan 2006 | |
| Sergei Haller (Giessen) | Comp. group theory | 16th Jan 2006 to 11th Jul 2007 | |
| Damien Stehlé (ENS, Lyon) | Lattices | 29th Jan 2006 to 28th Jan 2007 | |
| Jürgen Klüners (Kassel) | Number Theory | 2nd Feb 2006 to 22nd Mar 2006 | |
| Gabrielle Nebe (RWTH. Aachen) | Group Theory, Lattices | 13th Feb 2006 to 18th Mar 2006 | |
| Mark Watkins (Cambridge) | Arithmetic Geometry | 17th Mar 2006 to 19th Apr 2006 | |
| Tom Fisher (Cambridge) | Arithmetic Geometry | 20th Mar 2006 to 13th Apr 2006 | |
| Dan Roozemond (TU Eindhoven) | Lie Theory | 30th Apr 2006 to 31st Dec 2006 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 15th May 2006 to 12th Jun 2006 | |
| Tim Dokchitser (Cambridge) | L-Functions | 8th Aug 2006 to 17th Sep 2006 | |
| Jasper Scholten (Leuven) | Arithmetic Geometry | 2nd Sep 2006 to 1st Sep 2007 | |
| Frederik Vercauteren (Katholieke U. Leuven) | Cryptography | 2nd Sep 2006 to 28th Feb 2007 | |
| Gregor Kemper (TU Munich) | Commutative Algebra | 11th Sep 2006 to 29th Sep 2006 | |
| Eric Rains (Caltech) | Lie Theory | 4th Nov 2006 to 13th Nov 2006 | |
| Colva Roney-Dougal (St. Andrews) | Geometric Topology | 13th Nov 2006 to 1st Dec 2006 | |
| Mark Watkins (Bristol) | Analytic Number Theory | 26th Nov 2006 to 4th Feb 2007 | |
| Derek Holt (Warwick) | Group Theory | 3rd Jan 2007 to 17th Mar 2007 | |
| Peter Brooksbank (Bucknell) | Comp. group theory | 24th Jan 2007 to 2nd Feb 2007 | |
| Richard Brent (Oxford) | Number Theory, Computer Science | 11th Feb 2007 to 14th Jun 2007 | |
| Henrik Baarnhielm (QMUL) | Comp. group theory | 1st Apr 2007 to 16th May 2007 | |
| Willem de Graaf (Trento) | Lie Theory | 9th Apr 2007 to 8th Jun 2007 | |
| Charles Leedham-Greene (QMUL) | Group Theory | 15th Apr 2007 to 26th May 2007 | |
| Serena Cicalo (Trento) | 30th Apr 2007 to 23rd May 2007 | ||
| Christian Caranica (LSU, Baton Rouge) | Number Theory | 12th May 2007 to 30th Jun 2007 | |
| John Voight (Minnesota) | Arithmetic Geometry | 1st Jun 2007 to 19th Jun 2007 | |
| Peter Brooksbank (Bucknell) | Comp. group theory | 14th Jun 2007 to 2nd Jul 2007 | |
| Shuhong Gao (Clemson) | Commutative Algebra | 21st Jul 2007 to 27th Jul 2007 | |
| Tobias Beck (Linz) | Algebraic Geometry | 4th Aug 2007 to 2nd Sep 2007 | |
| Michael Vaughan-Lee (Oxford) | Group Theory | 11th Aug 2007 to 1st Sep 2007 | |
| Lassina Dembele (Warwick) | Arithmetic Geometry | 16th Aug 2007 to 16th Sep 2007 | |
| Mikael Johansson (Jena) | Homological Algebra | 14th Sep 2007 to 19th Oct 2007 | |
| Dimitri Leemans (Bruxelles Libre) | Group Theory, Incidence Geometry | 15th Sep 2007 to 12th Dec 2007 | |
| Markus Kirschmer (RWTH Aachen) | Group Theory, Lattices | 20th Sep 2007 to 3rd Nov 2007 | |
| Andrea Previtali (Como) | Representation Theory | 1st Oct 2007 to 28th Feb 2008 | |
| Damien Stehlé (ENS, Lyon) | Lattices | 10th Nov 2007 to 20th Jan 2008 | |
| Axel Kohnert (Bayreuth) | Combinatorics | 21st Jan 2008 | |
| Renate Schleidler (Calgary) | Cryptography | 23rd Jan 2008 | |
| Gabrielle Nebe (RWTH. Aachen) | Group Theory, Lattices | 2nd Feb 2008 to 2nd Mar 2008 | |
| Michael Pohst (TU Berlin) | Number Theory | 7th Feb 2008 to 1st Mar 2008 | |
| Peter Fleischmann (Kent) | Representation Theory, Invariant Theory | 9th Feb 2008 to 7th Mar 2008 | |
| Mark Watkins (Bristol) | Analytic Number Theory | 11th Feb 2008 to 1st Mar 2008 | |
| Matt Greenberg (Calgary) | Arithmetic Geometry | 21st Jul 2008 to 8th Aug 2008 | |
| Tim Dokchitser (Cambridge) | L-Functions | 24th Aug 2008 to 28th Sep 2008 | |
| Nicolas Brisebarre (ENS, Lyon) | Number Theory | 1st Sep 2008 to 1st Nov 2008 | |
| Angela Chin (Malaya) | Cohomology | 1st Sep 2008 to 30th Sep 2008 | |
| Lassina Dembele (Warwick) | Arithmetic Geometry | 1st Oct 2008 to 15th Nov 2008 | |
| Jon Carlson (Georgia, Athens) | Representation Theory | 8th Oct 2008 to 1st Nov 2008 | |
| Reinhard Laue (Bayreuth) | Combinatorics | 13th Jan 2009 to 17th Jan 2009 | |
| Gavin Brown (Kent) | Algebraic Geometry | 14th Jan 2009 to 11th Feb 2009 | |
| Alexander Kasprzyk (Kent) | Algebraic Geometry | 28th Jan 2009 to 7th Mar 2009 | |
| Jarosław Buczyński (Texas A&M) | Algebraic Geometry | 1st Feb 2009 to 14th Feb 2009 | |
| Ken Nakamula (Tokyo Metro) | Number Theory | 6th Feb 2009 to 16th Feb 2009 | |
| Richard Brent (ANU) | Number Theory, Computer Science | 9th Feb 2009 to 13th Feb 2009 | |
| Gerriet Moehlmann (TU Berlin) | Function fields | 22nd Feb 2009 to 28th Mar 2009 | |
| Jared Weinstein (UCLA) | Number Theory | 20th Apr 2009 to 15th May 2009 | |
| Dan Yasaki (Greensboro) | Number Theory | 22nd Apr 2009 to 19th May 2009 | |
| Robert Wilson (QMUL) | Representation Theory | 27th Apr 2009 to 5th Jun 2009 | |
| John Voight (Vermont) | Arithmetic Geometry | 12th May 2009 to 31st May 2009 | |
| Keiichiro Nishimoto (Tokyo Metro) | Number Theory | 2nd Jun 2009 to 15th Feb 2009 | |
| Nils Bruin (Simon Fraser) | Number Theory | 3rd Jun 2009 to 10th Jul 2009 | |
| Alexa van der Waall (Simon Fraser) | Differential Algebra | 3rd Jun 2009 to 30th Jul 2009 | |
| Peter Brooksbank (Bucknell) | Comp. group theory | 12th Jun 2009 to 10th Jul 2009 | |
| David Eisenbud (Berkeley) | Algebraic Geometry | 10th Jul 2009 to 16th Jul 2009 | |
| Damien Stehlé (CNRS, Lyon) | Lattices | 19th Jul 2009 to 30th Jun 2010 | |
| Ivan Morel (Coutelle student, Lyon) | Lattices | Aug 2009 to Jan 2010 | |
| Kamal Khuri-Makdisi (American University, Beirut) | Number Theory | 15th Aug 2009 to 15th Sep 2009 | |
| Derek Holt (Warwick) | Group Theory | 3rd Oct 2009 to 5th Dec 2009 | |
| Markus Kirschmer (RWTH Aachen) | Group Theory, Lattices | 3rd Oct 2009 to 1st May 2010 | |
| Jack Button (Cambridge) | Geometric Topology | 6th Oct 2009 to 31st Oct 2009 | |
| Doris Kern (TU, Berlin) | Comp. number theory | 21st Oct 2009 to 31st Oct 2009 | |
| Gavin Brown (Loughborough) | Algebraic Geometry | 14th Dec 2009 to 20th Jan 2010 |